1. Data Sources & Collection

CMS Nursing Home Provider Information - https://data.cms.gov/provider-data/dataset/4pq5-n9py (2017 - 2021)

CMS Medicare Claims Quality Measures - https://data.cms.gov/provider-data/dataset/ijh5-nb2v (April 2020 - March 2021)

CMS Survey Summary - https://data.cms.gov/provider-data/dataset/tbry-pc2d (2017 - 2020)

CMS MDS Quality Measures - https://data.cms.gov/provider-data/dataset/djen-97ju (April 2020 - March 2021)

CMS COVID-19 Nursing Home Data - https://data.cms.gov/covid-19/covid-19-nursing-home-data (April 2020 - December 2020, January 2021 - March 2021)

2. Construct dataset

import pandas as pd 
import numpy as np
import os 
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels.api as sm
import scipy.stats as stats

# Set directory
os.chdir('C:/Users/erpin/Documents/CIND820')

p = 'NH_ProviderInfo_Jan2022.csv'
s = 'NH_SurveySummary_Nov2021.csv'
m = 'NH_QualityMsr_MDS_Nov2021.csv'
c = 'NH_QualityMsr_Claims_Nov2021.csv'
cov = 'faclevel_2020.csv'

# Select columns from provider dataset
dfp = pd.read_csv(p, dtype={'Federal Provider Number':'str'}, encoding='cp1252')
colsp= [0,1,4,9,10,11,30,48,50,58,59,60,87,88,89]
dfp = dfp[dfp.columns[colsp]]
dfp['Federal Provider Number'] = dfp['Federal Provider Number'].apply(lambda x: x.lstrip('0'))

# Select columns from MDS dataset 
dfm = pd.read_csv(m, dtype={'Federal Provider Number':'str'}, encoding='cp1252')
LS = dfm[dfm['Resident type']== 'Long Stay']
colsm = [0,7,8,17]
LS = LS[LS.columns[colsm]]
LSpivot = LS.pivot(index=['Federal Provider Number', 'Resident type'], columns='Measure Description', values='Four Quarter Average Score')
LSpivot.reset_index(drop=False, inplace=True)
LSpivot['Federal Provider Number'] = LSpivot['Federal Provider Number'].apply(lambda x: x.lstrip('0'))

# Select columns from surveys dataset 
dfs = pd.read_csv(s, dtype={'Federal Provider Number':'str'}, encoding='cp1252')
colss = [0,6,7,9,10]
dfs = dfs[dfs.columns[colss]]
dfs = dfs[dfs['Inspection Cycle']==3]
dfs.to_csv('inspection.csv')
dfs['Federal Provider Number'] = dfs['Federal Provider Number'].apply(lambda x: x.lstrip('0'))

#select columns from COVID 2020 dataset 
dfcov = pd.read_csv(cov, dtype={'Federal Provider Number':'str'})
colcov = [1,13,19,22]
dfcov = dfcov[dfcov.columns[colcov]]
dfcov['Total Number of Occupied Beds'] = dfcov['Total Number of Occupied Beds'].replace(0, np.nan)
dfcov['Confirmed COVID-19 Cases Per Occupied Beds'] = dfcov['Residents Weekly Confirmed COVID-19']/dfcov['Total Number of Occupied Beds']
dfcov['COVID-19 Deaths Per Occupied Beds'] = dfcov['Residents Weekly COVID-19 Deaths']/dfcov['Total Number of Occupied Beds']
dfcovm = dfcov.groupby(['Federal Provider Number']).mean().reset_index()
dfcovm['Federal Provider Number'] = dfcovm['Federal Provider Number'].apply(lambda x: x.lstrip('0'))

#Select columns from claims dataset 
dfc = pd.read_csv(c, dtype={'Federal Provider Number':'str'}, encoding='cp1252')
dfc = dfc[dfc['Measure Description']=='Number of outpatient emergency department visits per 1000 long-stay resident days']
colc = [0,7,9]
dfc = dfc[dfc.columns[colc]]
dfc['Federal Provider Number'] = dfc['Federal Provider Number'].apply(lambda x: x.lstrip('0'))

df1 = pd.merge(dfp, LSpivot, on='Federal Provider Number', how='left')
df2 = pd.merge(df1, dfs, on='Federal Provider Number', how='left')
df3 = pd.merge(df2, dfcovm, on='Federal Provider Number', how='left')
final_df = pd.merge(df3, dfc, on='Federal Provider Number', how='left')

C:\Users\erpin\anaconda3\lib\site-packages\IPython\core\interactiveshell.py:3146: DtypeWarning: Columns (84,85) have mixed types.Specify dtype option on import or set low_memory=False.
  has_raised = await self.run_ast_nodes(code_ast.body, cell_name,

from IPython.core.display import display, HTML
display(HTML("<style>.container { width:100% !important; }</style>"))

3. Data Cleaning

#Checking columns 
final_df.columns.tolist()

['Federal Provider Number',
 'Provider Name',
 'Provider State',
 'Ownership Type',
 'Number of Certified Beds',
 'Average Number of Residents per Day',
 'Long-Stay QM Rating',
 'Total nursing staff turnover',
 'Registered Nurse turnover',
 'Adjusted Nurse Aide Staffing Hours per Resident per Day',
 'Adjusted LPN Staffing Hours per Resident per Day',
 'Adjusted RN Staffing Hours per Resident per Day',
 'Number of Facility Reported Incidents',
 'Number of Substantiated Complaints',
 'Number of Citations from Infection Control Inspections',
 'Resident type',
 'Percentage of high risk long-stay residents with pressure ulcers',
 'Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine',
 'Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine',
 'Percentage of long-stay residents experiencing one or more falls with major injury',
 'Percentage of long-stay residents who have depressive symptoms',
 'Percentage of long-stay residents who lose too much weight',
 'Percentage of long-stay residents who received an antianxiety or hypnotic medication',
 'Percentage of long-stay residents who received an antipsychotic medication',
 'Percentage of long-stay residents who were physically restrained',
 'Percentage of long-stay residents whose ability to move independently worsened',
 'Percentage of long-stay residents whose need for help with daily activities has increased',
 'Percentage of long-stay residents with a catheter inserted and left in their bladder',
 'Percentage of long-stay residents with a urinary tract infection',
 'Percentage of low risk long-stay residents who lose control of their bowels or bladder',
 'Inspection Cycle',
 'Health Survey Date',
 'Total Number of Health Deficiencies',
 'Total Number of Fire Safety Deficiencies',
 'Residents Weekly Confirmed COVID-19',
 'Residents Weekly COVID-19 Deaths',
 'Total Number of Occupied Beds',
 'Confirmed COVID-19 Cases Per Occupied Beds',
 'COVID-19 Deaths Per Occupied Beds',
 'Measure Description',
 'Adjusted Score']

# Rename 'Adjusted Score' to 'Number of outpatient emergency department visits per 1000 long-stay resident days'
final_df.rename(columns={'Adjusted Score': 'Number of outpatient emergency department visits per 1000 long-stay resident days'}, inplace=True)

#Remove unnecessary columns - Resident type, Inspection Cycle, Measure Description, Residents Weekly Confirmed COVID-19, Residents Weekly COVID-19 Deaths, Total Number of Occupied Beds
final_df.drop(['Resident type', 'Inspection Cycle', 'Measure Description', 'Residents Weekly Confirmed COVID-19', 'Residents Weekly COVID-19 Deaths', 'Total Number of Occupied Beds', 'Health Survey Date', 'Provider State'], axis=1, inplace=True)

# Count number of rows - 15238 
len(final_df.index)

15238

#Check for duplicate rows - No duplicates 
final_df[final_df['Federal Provider Number'].duplicated() == True].sort_values('Federal Provider Number')

	Federal Provider Number	Provider Name	Ownership Type	Number of Certified Beds	Average Number of Residents per Day	Long-Stay QM Rating	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	...	Percentage of long-stay residents whose ability to move independently worsened	Percentage of long-stay residents whose need for help with daily activities has increased	Percentage of long-stay residents with a catheter inserted and left in their bladder	Percentage of long-stay residents with a urinary tract infection	Percentage of low risk long-stay residents who lose control of their bowels or bladder	Total Number of Health Deficiencies	Total Number of Fire Safety Deficiencies	Confirmed COVID-19 Cases Per Occupied Beds	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days

0 rows × 33 columns

#Check for null values in dependent value - 2241 rows
final_df['Number of outpatient emergency department visits per 1000 long-stay resident days'].isna().sum()
#Remove 2241 rows with null dependent value 
mod_df = final_df.dropna(how='any', subset=['Number of outpatient emergency department visits per 1000 long-stay resident days'])

#Nulls per column 
colnulls = mod_df.isnull().sum(axis=0).to_frame(name='Column Nulls')

#Nulls per column 
colnulls = mod_df.isnull().sum(axis=0).to_frame(name='Column Nulls')
# Count nulls per row 
rownulls = mod_df.set_index('Provider Name').isnull().sum(axis=1)
rownulls.count()
rownulls[rownulls > 15].count()
rownulls.sort_values(ascending=False)

Provider Name
HEDDINGTON OAKS                                      20
GOLDEN CROSS HEALTH CARE                             20
GREENE COUNTY NURSING HOME                           20
THE VILLAGES OF GENERAL BAPTIST HEALTH CARE  EAST    20
ROLLING MEADOWS                                      17
                                                     ..
HARROGATE                                             0
LAKELAND HEALTH CARE CENTER                           0
ASPEN HILLS HEALTHCARE CENTER                         0
PROMEDICA SKILLED NURSING & REHAB - MOUNTAINSIDE      0
LIFE CARE CENTER OF SULLIVAN                          0
Length: 12997, dtype: int64

# Coding the 'Ownership' Categorical Variable in prepartion for dummy variable creation
mod_df['Ownership Type'].value_counts()
categorizing_ownership = {'Ownership Type': {
    'For profit - Corporation': 1, 
    'Non profit - Corporation': 0,
    'For profit - Limited Liability company': 1,
    'For profit - Individual': 1, 
    'For profit - Partnership': 1,
    'Government - County': 2,
    'Non profit - Church related': 0,
    'Non profit - Other': 0, 
    'Government - Hospital district': 2, 
    'Government - State': 2,
    'Government - City': 2, 
    'Government - City/county': 2,
    'Government - Federal': 2}}
mod_df = mod_df.replace(categorizing_ownership)
mod_df.head()

	Federal Provider Number	Provider Name	Ownership Type	Number of Certified Beds	Average Number of Residents per Day	Long-Stay QM Rating	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	...	Percentage of long-stay residents whose ability to move independently worsened	Percentage of long-stay residents whose need for help with daily activities has increased	Percentage of long-stay residents with a catheter inserted and left in their bladder	Percentage of long-stay residents with a urinary tract infection	Percentage of low risk long-stay residents who lose control of their bowels or bladder	Total Number of Health Deficiencies	Total Number of Fire Safety Deficiencies	Confirmed COVID-19 Cases Per Occupied Beds	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days
0	15009	BURNS NURSING HOME, INC.	1	57	53.2	5.0	NaN	NaN	NaN	NaN	...	28.180706	15.060243	0.738709	0.555555	66.000001	0.0	2.0	0.032987	0.003443	0.272998
1	15010	COOSA VALLEY HEALTHCARE CENTER	1	85	79.8	2.0	52.4	21.4	2.49541	0.83163	...	14.764966	8.837209	2.067165	4.016065	42.857145	7.0	3.0	0.008493	0.000963	0.481088
2	15012	HIGHLANDS HEALTH AND REHAB	2	50	39.9	3.0	NaN	NaN	NaN	NaN	...	31.351583	12.500002	4.839041	11.016951	75.471696	5.0	0.0	0.009605	0.003024	0.988491
3	15014	EASTVIEW REHABILITATION & HEALTHCARE CENTER	1	92	69.4	2.0	NaN	NaN	2.02560	0.98558	...	36.218930	21.198155	2.700401	7.251909	33.333335	6.0	5.0	0.014678	0.000000	0.866367
4	15015	PLANTATION MANOR NURSING HOME	1	103	72.4	3.0	51.3	60.0	2.36250	1.28006	...	10.404354	10.599077	0.560731	3.767122	32.323234	7.0	4.0	0.004360	0.000000	0.640404

5 rows × 33 columns

#Create dummy variables 
clean_df = pd.get_dummies(mod_df, columns=['Ownership Type', 'Long-Stay QM Rating'])
clean_df.head()

	Federal Provider Number	Provider Name	Number of Certified Beds	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	...	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days	Ownership Type_0	Ownership Type_1	Ownership Type_2	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0	Long-Stay QM Rating_5.0
0	15009	BURNS NURSING HOME, INC.	57	53.2	NaN	NaN	NaN	NaN	NaN	0	...	0.003443	0.272998	0	1	0	0	0	0	0	1
1	15010	COOSA VALLEY HEALTHCARE CENTER	85	79.8	52.4	21.4	2.49541	0.83163	1.17810	0	...	0.000963	0.481088	0	1	0	0	1	0	0	0
2	15012	HIGHLANDS HEALTH AND REHAB	50	39.9	NaN	NaN	NaN	NaN	NaN	0	...	0.003024	0.988491	0	0	1	0	0	1	0	0
3	15014	EASTVIEW REHABILITATION & HEALTHCARE CENTER	92	69.4	NaN	NaN	2.02560	0.98558	0.53602	0	...	0.000000	0.866367	0	1	0	0	1	0	0	0
4	15015	PLANTATION MANOR NURSING HOME	103	72.4	51.3	60.0	2.36250	1.28006	0.50438	0	...	0.000000	0.640404	0	1	0	0	0	1	0	0

5 rows × 39 columns

4.Data Exploration & Pre-processing

#Dataset shape
clean_df.shape

(12997, 39)

#Dataset info 
clean_df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 12997 entries, 0 to 15235
Data columns (total 39 columns):
 #   Column                                                                                             Non-Null Count  Dtype  
---  ------                                                                                             --------------  -----  
 0   Federal Provider Number                                                                            12997 non-null  object 
 1   Provider Name                                                                                      12997 non-null  object 
 2   Number of Certified Beds                                                                           12997 non-null  int64  
 3   Average Number of Residents per Day                                                                12973 non-null  float64
 4   Total nursing staff turnover                                                                       11052 non-null  float64
 5   Registered Nurse turnover                                                                          10350 non-null  float64
 6   Adjusted Nurse Aide Staffing Hours per Resident per Day                                            12645 non-null  float64
 7   Adjusted LPN Staffing Hours per Resident per Day                                                   12645 non-null  float64
 8   Adjusted RN Staffing Hours per Resident per Day                                                    12645 non-null  float64
 9   Number of Facility Reported Incidents                                                              12997 non-null  int64  
 10  Number of Substantiated Complaints                                                                 12997 non-null  int64  
 11  Number of Citations from Infection Control Inspections                                             12993 non-null  float64
 12  Percentage of high risk long-stay residents with pressure ulcers                                   12960 non-null  float64
 13  Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine        12991 non-null  float64
 14  Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine  12996 non-null  float64
 15  Percentage of long-stay residents experiencing one or more falls with major injury                 12991 non-null  float64
 16  Percentage of long-stay residents who have depressive symptoms                                     12986 non-null  float64
 17  Percentage of long-stay residents who lose too much weight                                         12981 non-null  float64
 18  Percentage of long-stay residents who received an antianxiety or hypnotic medication               12990 non-null  float64
 19  Percentage of long-stay residents who received an antipsychotic medication                         12973 non-null  float64
 20  Percentage of long-stay residents who were physically restrained                                   12989 non-null  float64
 21  Percentage of long-stay residents whose ability to move independently worsened                     12918 non-null  float64
 22  Percentage of long-stay residents whose need for help with daily activities has increased          12979 non-null  float64
 23  Percentage of long-stay residents with a catheter inserted and left in their bladder               12986 non-null  float64
 24  Percentage of long-stay residents with a urinary tract infection                                   12987 non-null  float64
 25  Percentage of low risk long-stay residents who lose control of their bowels or bladder             12764 non-null  float64
 26  Total Number of Health Deficiencies                                                                12900 non-null  float64
 27  Total Number of Fire Safety Deficiencies                                                           12883 non-null  float64
 28  Confirmed COVID-19 Cases Per Occupied Beds                                                         12900 non-null  float64
 29  COVID-19 Deaths Per Occupied Beds                                                                  12900 non-null  float64
 30  Number of outpatient emergency department visits per 1000 long-stay resident days                  12997 non-null  float64
 31  Ownership Type_0                                                                                   12997 non-null  uint8  
 32  Ownership Type_1                                                                                   12997 non-null  uint8  
 33  Ownership Type_2                                                                                   12997 non-null  uint8  
 34  Long-Stay QM Rating_1.0                                                                            12997 non-null  uint8  
 35  Long-Stay QM Rating_2.0                                                                            12997 non-null  uint8  
 36  Long-Stay QM Rating_3.0                                                                            12997 non-null  uint8  
 37  Long-Stay QM Rating_4.0                                                                            12997 non-null  uint8  
 38  Long-Stay QM Rating_5.0                                                                            12997 non-null  uint8  
dtypes: float64(26), int64(3), object(2), uint8(8)
memory usage: 3.3+ MB

Both Total nursing staff turnover and Registered Nurse turnover attributes have a large, but acceptable number of nulls from 1000-2000 rows.

#Describe dataset 
clean_df.describe()
# .to_csv("DescribeDataset.csv")

	Number of Certified Beds	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	Number of Substantiated Complaints	Number of Citations from Infection Control Inspections	...	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days	Ownership Type_0	Ownership Type_1	Ownership Type_2	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0	Long-Stay QM Rating_5.0
count	12997.000000	12973.000000	11052.000000	10350.000000	12645.000000	12645.000000	12645.000000	12997.000000	12997.000000	12993.000000	...	12900.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000
mean	113.143649	81.455230	51.273127	49.536705	2.171593	0.870455	0.675686	1.539432	4.832808	1.357269	...	0.003258	0.701247	0.221282	0.713549	0.065169	0.091790	0.149034	0.174733	0.222282	0.353081
std	59.809910	46.666475	15.068248	21.247156	0.584521	0.339521	0.403360	3.578529	9.157541	2.368291	...	0.004708	0.480244	0.415126	0.452120	0.246833	0.288741	0.356136	0.379753	0.415796	0.477946
min	18.000000	1.000000	6.100000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	74.000000	51.000000	40.900000	33.300000	1.788230	0.648650	0.400500	0.000000	0.000000	0.000000	...	0.000313	0.364782	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
50%	104.000000	73.700000	50.700000	50.000000	2.110130	0.853320	0.585050	0.000000	2.000000	1.000000	...	0.002016	0.595768	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
75%	132.000000	99.300000	60.900000	64.000000	2.495520	1.073060	0.855110	2.000000	5.000000	2.000000	...	0.004805	0.922189	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000
max	874.000000	703.300000	100.000000	100.000000	6.903020	3.636150	5.580270	72.000000	162.000000	43.000000	...	0.263780	5.477409	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000

8 rows × 37 columns

Distributions

# Visualize distributions
clean_df.hist(bins=30, figsize=(30,25), layout=(13,3));

On visual inspection, it can be noted that ~15 plots are approximately normally distributed, however a number of attributes are not normally distributed or have notably long right- or left-tails. This will be further addressed in assumption testing.

Outlier Detection

Since the data was manually reported by nursing homes regarding their performance, a cautious approach will be taken for outlier detection and removal.

#Visualizing outliers 
outlier_df = clean_df.drop(['Federal Provider Number', 'Provider Name'], axis=1).copy()
for i in outlier_df:
    plt.figure()
    outlier_df.boxplot([i])

<ipython-input-23-e1c281880675>:4: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
  plt.figure()

On visual analysis, there are a varying amount of outliers in each attribute, however the majority of attributes have outliers on one-tail, resulting in skew. To quantify this, the skewness will be calculated below:

#Evaluating skewness of attributes 
outlier_df.skew()

Number of Certified Beds                                                                              2.814405
Average Number of Residents per Day                                                                   2.784565
Total nursing staff turnover                                                                          0.356678
Registered Nurse turnover                                                                             0.149541
Adjusted Nurse Aide Staffing Hours per Resident per Day                                               0.709330
Adjusted LPN Staffing Hours per Resident per Day                                                      0.584469
Adjusted RN Staffing Hours per Resident per Day                                                       1.922657
Number of Facility Reported Incidents                                                                 5.765617
Number of Substantiated Complaints                                                                    4.545777
Number of Citations from Infection Control Inspections                                                4.017724
Percentage of high risk long-stay residents with pressure ulcers                                      0.891290
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine          -3.197396
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine    -3.938107
Percentage of long-stay residents experiencing one or more falls with major injury                    1.146353
Percentage of long-stay residents who have depressive symptoms                                        3.685780
Percentage of long-stay residents who lose too much weight                                            0.974590
Percentage of long-stay residents who received an antianxiety or hypnotic medication                  0.825813
Percentage of long-stay residents who received an antipsychotic medication                            2.149230
Percentage of long-stay residents who were physically restrained                                     36.761392
Percentage of long-stay residents whose ability to move independently worsened                        0.462988
Percentage of long-stay residents whose need for help with daily activities has increased             0.481214
Percentage of long-stay residents with a catheter inserted and left in their bladder                  2.690169
Percentage of long-stay residents with a urinary tract infection                                      2.122940
Percentage of low risk long-stay residents who lose control of their bowels or bladder                0.009498
Total Number of Health Deficiencies                                                                   1.495910
Total Number of Fire Safety Deficiencies                                                              1.749042
Confirmed COVID-19 Cases Per Occupied Beds                                                            8.727233
COVID-19 Deaths Per Occupied Beds                                                                    15.602656
Number of outpatient emergency department visits per 1000 long-stay resident days                     1.561035
Ownership Type_0                                                                                      1.343020
Ownership Type_1                                                                                     -0.944803
Ownership Type_2                                                                                      3.523822
Long-Stay QM Rating_1.0                                                                               2.827949
Long-Stay QM Rating_2.0                                                                               1.971267
Long-Stay QM Rating_3.0                                                                               1.713311
Long-Stay QM Rating_4.0                                                                               1.336044
Long-Stay QM Rating_5.0                                                                               0.614886
dtype: float64

There is a significant amount of skew in 9 numeric attributes. To address this, right-skewed attributes values with a skew > 3 greater will have values greater than the 90th percentile replaced by the median. Left-skewed values with a skew < -3 will have values less than the 10th percentile replaced by the median. Categorical dummy variables will not be included.

#Addressing skew and testing resulting skewness 
Q10 = outlier_df.quantile(0.1)
Q50 = outlier_df.quantile(0.5)
Q90 = outlier_df.quantile(0.9)
outlier_df['Number of Facility Reported Incidents'] = np.where(outlier_df['Number of Facility Reported Incidents'] > Q90['Number of Facility Reported Incidents'], Q50['Number of Facility Reported Incidents'], outlier_df['Number of Facility Reported Incidents'])
outlier_df['Number of Substantiated Complaints'] = np.where(outlier_df['Number of Substantiated Complaints'] > Q90['Number of Substantiated Complaints'], Q50['Number of Substantiated Complaints'], outlier_df['Number of Substantiated Complaints'])
outlier_df['Number of Citations from Infection Control Inspections'] = np.where(outlier_df['Number of Citations from Infection Control Inspections'] > Q90['Number of Citations from Infection Control Inspections'], Q50['Number of Citations from Infection Control Inspections'], outlier_df['Number of Citations from Infection Control Inspections'])
outlier_df['Percentage of long-stay residents who have depressive symptoms'] = np.where(outlier_df['Percentage of long-stay residents who have depressive symptoms'] > Q90['Percentage of long-stay residents who have depressive symptoms'], Q50['Percentage of long-stay residents who have depressive symptoms'], outlier_df['Percentage of long-stay residents who have depressive symptoms'])
outlier_df['Percentage of long-stay residents who were physically restrained'] = np.where(outlier_df['Percentage of long-stay residents who were physically restrained'] > Q90['Percentage of long-stay residents who were physically restrained'], Q50['Percentage of long-stay residents who were physically restrained'], outlier_df['Percentage of long-stay residents who were physically restrained'])
outlier_df['Confirmed COVID-19 Cases Per Occupied Beds'] = np.where(outlier_df['Confirmed COVID-19 Cases Per Occupied Beds'] > Q90['Confirmed COVID-19 Cases Per Occupied Beds'], Q50['Confirmed COVID-19 Cases Per Occupied Beds'], outlier_df['Confirmed COVID-19 Cases Per Occupied Beds'])
outlier_df['COVID-19 Deaths Per Occupied Beds'] = np.where(outlier_df['COVID-19 Deaths Per Occupied Beds'] > Q90['COVID-19 Deaths Per Occupied Beds'], Q50['COVID-19 Deaths Per Occupied Beds'], outlier_df['COVID-19 Deaths Per Occupied Beds'])
outlier_df['Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine'] = np.where(outlier_df['Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine'] < Q10['Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine'], Q50['Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine'], outlier_df['Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine'])
outlier_df['Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine'] = np.where(outlier_df['Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine'] < Q10['Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine'], Q50['Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine'], outlier_df['Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine'])
outlier_df.skew()

Number of Certified Beds                                                                             2.814405
Average Number of Residents per Day                                                                  2.784565
Total nursing staff turnover                                                                         0.356678
Registered Nurse turnover                                                                            0.149541
Adjusted Nurse Aide Staffing Hours per Resident per Day                                              0.709330
Adjusted LPN Staffing Hours per Resident per Day                                                     0.584469
Adjusted RN Staffing Hours per Resident per Day                                                      1.922657
Number of Facility Reported Incidents                                                                1.761081
Number of Substantiated Complaints                                                                   1.596168
Number of Citations from Infection Control Inspections                                               1.273226
Percentage of high risk long-stay residents with pressure ulcers                                     0.891290
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine         -1.877671
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine   -1.249275
Percentage of long-stay residents experiencing one or more falls with major injury                   1.146353
Percentage of long-stay residents who have depressive symptoms                                       1.671901
Percentage of long-stay residents who lose too much weight                                           0.974590
Percentage of long-stay residents who received an antianxiety or hypnotic medication                 0.825813
Percentage of long-stay residents who received an antipsychotic medication                           2.149230
Percentage of long-stay residents who were physically restrained                                     0.000000
Percentage of long-stay residents whose ability to move independently worsened                       0.462988
Percentage of long-stay residents whose need for help with daily activities has increased            0.481214
Percentage of long-stay residents with a catheter inserted and left in their bladder                 2.690169
Percentage of long-stay residents with a urinary tract infection                                     2.122940
Percentage of low risk long-stay residents who lose control of their bowels or bladder               0.009498
Total Number of Health Deficiencies                                                                  1.495910
Total Number of Fire Safety Deficiencies                                                             1.749042
Confirmed COVID-19 Cases Per Occupied Beds                                                           0.164549
COVID-19 Deaths Per Occupied Beds                                                                    0.865815
Number of outpatient emergency department visits per 1000 long-stay resident days                    1.561035
Ownership Type_0                                                                                     1.343020
Ownership Type_1                                                                                    -0.944803
Ownership Type_2                                                                                     3.523822
Long-Stay QM Rating_1.0                                                                              2.827949
Long-Stay QM Rating_2.0                                                                              1.971267
Long-Stay QM Rating_3.0                                                                              1.713311
Long-Stay QM Rating_4.0                                                                              1.336044
Long-Stay QM Rating_5.0                                                                              0.614886
dtype: float64

outlier_df.describe()

	Number of Certified Beds	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	Number of Substantiated Complaints	Number of Citations from Infection Control Inspections	...	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days	Ownership Type_0	Ownership Type_1	Ownership Type_2	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0	Long-Stay QM Rating_5.0
count	12997.000000	12973.000000	11052.000000	10350.000000	12645.000000	12645.000000	12645.000000	12997.000000	12997.000000	12993.000000	...	12900.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000
mean	113.143649	81.455230	51.273127	49.536705	2.171593	0.870455	0.675686	0.611834	2.417481	0.859309	...	0.002229	0.701247	0.221282	0.713549	0.065169	0.091790	0.149034	0.174733	0.222282	0.353081
std	59.809910	46.666475	15.068248	21.247156	0.584521	0.339521	0.403360	1.054702	3.017783	1.072238	...	0.002134	0.480244	0.415126	0.452120	0.246833	0.288741	0.356136	0.379753	0.415796	0.477946
min	18.000000	1.000000	6.100000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	74.000000	51.000000	40.900000	33.300000	1.788230	0.648650	0.400500	0.000000	0.000000	0.000000	...	0.000313	0.364782	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
50%	104.000000	73.700000	50.700000	50.000000	2.110130	0.853320	0.585050	0.000000	2.000000	1.000000	...	0.002016	0.595768	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
75%	132.000000	99.300000	60.900000	64.000000	2.495520	1.073060	0.855110	1.000000	3.000000	1.000000	...	0.003504	0.922189	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000
max	874.000000	703.300000	100.000000	100.000000	6.903020	3.636150	5.580270	4.000000	13.000000	4.000000	...	0.007999	5.477409	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000

8 rows × 37 columns

Dataset Normalization

Upon visual analysis of the data description, it is apparently that the scale of the various attributes varies significantly. It is imperative that the data be normalized.

#Data Normalization using the min-max method 
normalized_df = outlier_df.copy()
for column in normalized_df.columns:
    normalized_df[column] = (normalized_df[column] - normalized_df[column].min())/(normalized_df[column].max() - normalized_df[column].min())

normalized_df.describe()

	Number of Certified Beds	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	Number of Substantiated Complaints	Number of Citations from Infection Control Inspections	...	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days	Ownership Type_0	Ownership Type_1	Ownership Type_2	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0	Long-Stay QM Rating_5.0
count	12997.000000	12973.000000	11052.000000	10350.000000	12645.000000	12645.000000	12645.000000	12997.000000	12997.000000	12993.000000	...	12900.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000	12997.000000
mean	0.111149	0.114560	0.481077	0.495367	0.314586	0.239389	0.121085	0.152958	0.185960	0.214827	...	0.278669	0.128025	0.221282	0.713549	0.065169	0.091790	0.149034	0.174733	0.222282	0.353081
std	0.069871	0.066448	0.160471	0.212472	0.084676	0.093374	0.072283	0.263675	0.232137	0.268059	...	0.266738	0.087677	0.415126	0.452120	0.246833	0.288741	0.356136	0.379753	0.415796	0.477946
min	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	0.065421	0.071195	0.370607	0.333000	0.259050	0.178389	0.071771	0.000000	0.000000	0.000000	...	0.039065	0.066598	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
50%	0.100467	0.103517	0.474973	0.500000	0.305682	0.234677	0.104843	0.000000	0.153846	0.250000	...	0.252043	0.108768	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
75%	0.133178	0.139969	0.583600	0.640000	0.361511	0.295109	0.153238	0.250000	0.230769	0.250000	...	0.438009	0.168362	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000
max	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	...	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000

8 rows × 37 columns

Dataset is normalized to [0,1]

5. Assumption Testing - Linear Regression

Normality of Predictor Distributions

# Visualize distributions
normalized_df.hist(bins=30, figsize=(30,25), layout=(13,3));

As stated above, ~15 plots are approximately normally distributed, however a number of attributes are not normally distributed or have notably long right- or left-tails. The variables that are not normally distributed will be log transformed to try to address skew.

Log Transformation of independent variables

#Identify and transform non-normal columns 
normalized_df[['Number of Facility Reported Incidents', 
         'Number of Substantiated Complaints',
         'Number of Citations from Infection Control Inspections',
         'Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine',
         'Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine',
         'Percentage of long-stay residents who have depressive symptoms',
         'Percentage of long-stay residents who were physically restrained',
         'Percentage of long-stay residents with a catheter inserted and left in their bladder',
         'Percentage of long-stay residents with a urinary tract infection',
         'Total Number of Health Deficiencies',
         'Total Number of Fire Safety Deficiencies',
         'Confirmed COVID-19 Cases Per Occupied Beds',
         'COVID-19 Deaths Per Occupied Beds']] = clean_df[['Number of Facility Reported Incidents', 
         'Number of Substantiated Complaints',
         'Number of Citations from Infection Control Inspections',
         'Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine',
         'Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine',
         'Percentage of long-stay residents who have depressive symptoms',
         'Percentage of long-stay residents who were physically restrained',
         'Percentage of long-stay residents with a catheter inserted and left in their bladder',
         'Percentage of long-stay residents with a urinary tract infection',
         'Total Number of Health Deficiencies',
         'Total Number of Fire Safety Deficiencies',
         'Confirmed COVID-19 Cases Per Occupied Beds',
         'COVID-19 Deaths Per Occupied Beds']].applymap(lambda x: np.log(1+x))

#Check distributions of transformed data set
normalized_df.hist(bins=30, figsize=(30,25), layout=(13,3));

After transformation, distributions remain non-normal for multiple attributes.

Linearity

g = sns.pairplot(normalized_df)

On visual inspection, linearity between the dependent variable and the independent variables does not exist for any attribute.

#Checking linearity between the independent and dependent variables using Pearson's coefficient
normalized_df.corr()['Number of outpatient emergency department visits per 1000 long-stay resident days']

Number of Certified Beds                                                                            -0.125236
Average Number of Residents per Day                                                                 -0.189076
Total nursing staff turnover                                                                         0.196617
Registered Nurse turnover                                                                            0.136190
Adjusted Nurse Aide Staffing Hours per Resident per Day                                             -0.026672
Adjusted LPN Staffing Hours per Resident per Day                                                     0.007379
Adjusted RN Staffing Hours per Resident per Day                                                     -0.147622
Number of Facility Reported Incidents                                                               -0.001510
Number of Substantiated Complaints                                                                   0.059976
Number of Citations from Infection Control Inspections                                               0.048291
Percentage of high risk long-stay residents with pressure ulcers                                     0.107017
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine         -0.057947
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine   -0.053029
Percentage of long-stay residents experiencing one or more falls with major injury                   0.141214
Percentage of long-stay residents who have depressive symptoms                                       0.031978
Percentage of long-stay residents who lose too much weight                                           0.059355
Percentage of long-stay residents who received an antianxiety or hypnotic medication                 0.152672
Percentage of long-stay residents who received an antipsychotic medication                           0.066667
Percentage of long-stay residents who were physically restrained                                     0.021778
Percentage of long-stay residents whose ability to move independently worsened                       0.007588
Percentage of long-stay residents whose need for help with daily activities has increased            0.120714
Percentage of long-stay residents with a catheter inserted and left in their bladder                 0.090871
Percentage of long-stay residents with a urinary tract infection                                     0.107932
Percentage of low risk long-stay residents who lose control of their bowels or bladder              -0.138148
Total Number of Health Deficiencies                                                                  0.016577
Total Number of Fire Safety Deficiencies                                                             0.018007
Confirmed COVID-19 Cases Per Occupied Beds                                                           0.064137
COVID-19 Deaths Per Occupied Beds                                                                    0.017457
Number of outpatient emergency department visits per 1000 long-stay resident days                    1.000000
Ownership Type_0                                                                                    -0.108730
Ownership Type_1                                                                                     0.088029
Ownership Type_2                                                                                     0.021620
Long-Stay QM Rating_1.0                                                                              0.329353
Long-Stay QM Rating_2.0                                                                              0.178982
Long-Stay QM Rating_3.0                                                                              0.036916
Long-Stay QM Rating_4.0                                                                             -0.070261
Long-Stay QM Rating_5.0                                                                             -0.306295
Name: Number of outpatient emergency department visits per 1000 long-stay resident days, dtype: float64

Examination of Pearson's coefficient against the dependent variable confirms a general lack of linearity in the model.
Based on this, it could be stated that the Assumption of Linearity is not fulfilled and that the regression model may not be able to efficiently explain the data.

Multicollinearity

corr = normalized_df.corr()
corr

	Number of Certified Beds	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	Number of Substantiated Complaints	Number of Citations from Infection Control Inspections	...	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days	Ownership Type_0	Ownership Type_1	Ownership Type_2	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0	Long-Stay QM Rating_5.0
Number of Certified Beds	1.000000	0.900118	-0.126293	-0.021561	-0.147186	-0.004918	-0.179360	0.107649	0.208205	0.124940	...	0.004811	-0.125236	-0.074621	0.055226	0.024342	-0.060794	-0.052735	-0.014243	-0.000956	0.084292
Average Number of Residents per Day	0.900118	1.000000	-0.191872	-0.062282	-0.144181	-0.051727	-0.184889	0.097875	0.155956	0.083070	...	-0.022466	-0.189076	-0.056577	0.054321	-0.004332	-0.098137	-0.075848	-0.033587	0.003190	0.140999
Total nursing staff turnover	-0.126293	-0.191872	1.000000	0.673395	-0.153107	-0.004462	-0.200957	0.089765	0.252349	0.176099	...	0.027915	0.196617	-0.142873	0.158201	-0.049666	0.141423	0.083499	0.064047	-0.013288	-0.191644
Registered Nurse turnover	-0.021561	-0.062282	0.673395	1.000000	-0.127903	0.089900	-0.311956	0.132674	0.276417	0.203330	...	0.023027	0.136190	-0.159292	0.188959	-0.078807	0.093750	0.046667	0.027324	-0.020436	-0.101795
Adjusted Nurse Aide Staffing Hours per Resident per Day	-0.147186	-0.144181	-0.153107	-0.127903	1.000000	0.215865	0.372787	0.004734	-0.189711	-0.062760	...	-0.054227	-0.026672	0.201623	-0.263516	0.144783	0.010851	-0.004440	-0.014332	-0.008354	0.015866
Adjusted LPN Staffing Hours per Resident per Day	-0.004918	-0.051727	-0.004462	0.089900	0.215865	1.000000	-0.216229	0.026374	-0.028365	0.021128	...	0.001224	0.007379	-0.009437	0.003206	0.010171	0.035162	-0.000327	-0.014127	-0.019080	0.004862
Adjusted RN Staffing Hours per Resident per Day	-0.179360	-0.184889	-0.200957	-0.311956	0.372787	-0.216229	1.000000	-0.041691	-0.226118	-0.153352	...	-0.006473	-0.147622	0.327438	-0.370488	0.128430	-0.061587	-0.033653	0.016984	0.038566	0.017473
Number of Facility Reported Incidents	0.107649	0.097875	0.089765	0.132674	0.004734	0.026374	-0.041691	1.000000	0.382498	0.205706	...	-0.007285	-0.001510	-0.080214	0.061315	0.022594	-0.034526	-0.006399	-0.006873	0.007252	0.014969
Number of Substantiated Complaints	0.208205	0.155956	0.252349	0.276417	-0.189711	-0.028365	-0.226118	0.382498	1.000000	0.398951	...	0.040112	0.059976	-0.191586	0.217728	-0.076597	0.003717	-0.006608	0.002133	-0.028402	0.009778
Number of Citations from Infection Control Inspections	0.124940	0.083070	0.176099	0.203330	-0.062760	0.021128	-0.153352	0.205706	0.398951	1.000000	...	0.045110	0.048291	-0.112366	0.110404	-0.013239	0.022968	0.010546	0.003653	-0.009102	-0.028530
Percentage of high risk long-stay residents with pressure ulcers	0.115988	0.087770	0.130029	0.145326	-0.090675	0.066424	-0.148458	0.027547	0.152409	0.055690	...	0.030034	0.107017	-0.102477	0.130944	-0.067503	0.175154	0.125516	0.033275	-0.032457	-0.201416
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.083332	-0.059052	-0.129610	-0.130713	0.122684	0.058968	0.102486	-0.018327	-0.178960	-0.108767	...	-0.014237	-0.057947	0.068126	-0.091680	0.053380	-0.071338	-0.039470	-0.023082	0.006081	0.095096
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.039580	-0.018108	-0.154718	-0.161003	0.114124	0.059335	0.083089	-0.044478	-0.187975	-0.108438	...	-0.036239	-0.053029	0.061487	-0.087454	0.056777	-0.058549	-0.043212	-0.042922	0.012519	0.100820
Percentage of long-stay residents experiencing one or more falls with major injury	-0.158051	-0.173738	0.079871	-0.021539	0.049911	-0.052541	0.100638	-0.089526	-0.138784	-0.053726	...	0.017350	0.141214	0.125053	-0.142830	0.051319	0.168642	0.133639	0.078794	-0.005306	-0.261918
Percentage of long-stay residents who have depressive symptoms	0.037086	0.044224	0.057616	0.033721	-0.161490	-0.183081	-0.074060	0.017777	0.131476	0.011295	...	-0.006276	0.031978	-0.065880	0.053770	0.012330	0.003360	0.004964	0.002113	-0.025316	0.012659
Percentage of long-stay residents who lose too much weight	0.016254	0.008257	0.103318	0.079098	-0.084411	0.023689	-0.067977	-0.003605	0.058816	0.030736	...	0.084037	0.059355	-0.012325	0.033521	-0.040702	0.108484	0.067021	0.055249	-0.005567	-0.154172
Percentage of long-stay residents who received an antianxiety or hypnotic medication	-0.071126	-0.107252	0.137401	0.057286	-0.069768	0.028015	-0.158831	-0.079134	-0.045466	0.002917	...	-0.011399	0.152672	-0.109651	0.089968	0.019675	0.132254	0.083700	0.034914	-0.018922	-0.157237
Percentage of long-stay residents who received an antipsychotic medication	-0.029395	-0.036698	0.038484	0.004690	-0.027251	-0.083068	0.000320	0.011696	-0.017123	0.019544	...	0.000723	0.066667	-0.022976	0.005061	0.029391	0.193346	0.127662	0.061255	-0.009726	-0.256726
Percentage of long-stay residents who were physically restrained	0.015216	0.015227	-0.031433	-0.022677	0.036444	0.045640	-0.015159	0.023571	-0.037907	-0.012107	...	-0.020756	0.021778	-0.004388	-0.022139	0.047964	0.033118	0.022377	0.014405	-0.015186	-0.035933
Percentage of long-stay residents whose ability to move independently worsened	-0.020046	-0.047750	0.117766	0.078569	-0.062003	0.013485	0.049939	0.005155	0.023547	0.008161	...	0.028389	0.007588	0.067181	-0.040758	-0.038382	0.229145	0.215771	0.156503	0.010947	-0.438709
Percentage of long-stay residents whose need for help with daily activities has increased	-0.039799	-0.092742	0.214752	0.158103	-0.077398	-0.023241	-0.095428	-0.039011	0.007915	0.056317	...	0.056563	0.120714	-0.026198	0.014281	0.017945	0.307158	0.243323	0.140147	-0.015489	-0.474403
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.045605	-0.069532	0.027325	-0.012917	0.072739	0.009525	0.051690	0.002416	-0.025569	-0.005524	...	0.011071	0.090871	0.058968	-0.065304	0.020449	0.217557	0.151358	0.073670	-0.018578	-0.289571
Percentage of long-stay residents with a urinary tract infection	-0.102895	-0.129016	0.011470	-0.078260	0.118544	0.009617	0.165595	-0.096640	-0.175337	-0.097245	...	-0.005685	0.107932	0.159763	-0.181862	0.064441	0.234208	0.161298	0.085516	-0.006437	-0.322525
Percentage of low risk long-stay residents who lose control of their bowels or bladder	0.034256	0.044325	-0.064327	-0.034825	-0.055871	-0.001356	0.149545	-0.041566	-0.089353	-0.032512	...	0.047690	-0.138148	0.170979	-0.157267	0.000872	-0.043740	-0.015232	0.029191	0.043897	-0.017301
Total Number of Health Deficiencies	0.076512	0.037216	0.090465	0.124462	-0.058827	0.018484	-0.096573	0.239879	0.343492	0.198937	...	0.017170	0.016577	-0.113887	0.120616	-0.029337	-0.011519	-0.028208	0.003160	-0.012856	0.024243
Total Number of Fire Safety Deficiencies	0.005505	-0.033827	0.090809	0.067496	-0.019676	-0.061777	-0.056070	0.120391	0.196644	0.036202	...	-0.018731	0.018007	-0.026995	0.017214	0.013945	0.000457	-0.001767	-0.006836	-0.021027	0.018988
Confirmed COVID-19 Cases Per Occupied Beds	-0.013455	-0.041030	0.114679	0.076710	-0.092332	0.024715	-0.111700	0.013506	0.074327	0.082561	...	0.646787	0.064137	-0.099031	0.114828	-0.043758	0.041257	0.039751	0.013945	-0.022201	-0.049230
COVID-19 Deaths Per Occupied Beds	0.004811	-0.022466	0.027915	0.023027	-0.054227	0.001224	-0.006473	-0.007285	0.040112	0.045110	...	1.000000	0.017457	-0.002562	0.014314	-0.021902	0.011282	0.022185	0.009740	-0.011606	-0.024869
Number of outpatient emergency department visits per 1000 long-stay resident days	-0.125236	-0.189076	0.196617	0.136190	-0.026672	0.007379	-0.147622	-0.001510	0.059976	0.048291	...	0.017457	1.000000	-0.108730	0.088029	0.021620	0.329353	0.178982	0.036916	-0.070261	-0.306295
Ownership Type_0	-0.074621	-0.056577	-0.142873	-0.159292	0.201623	-0.009437	0.327438	-0.080214	-0.191586	-0.112366	...	-0.002562	-0.108730	1.000000	-0.841337	-0.140746	-0.008338	-0.002927	0.030491	0.004332	-0.014529
Ownership Type_1	0.055226	0.054321	0.158201	0.188959	-0.263516	0.003206	-0.370488	0.061315	0.217728	0.110404	...	0.014314	0.088029	-0.841337	1.000000	-0.416716	0.009275	-0.008193	-0.030686	-0.012461	0.029741
Ownership Type_2	0.024342	-0.004332	-0.049666	-0.078807	0.144783	0.010171	0.128430	0.022594	-0.076597	-0.013239	...	-0.021902	0.021620	-0.140746	-0.416716	1.000000	-0.002965	0.019929	0.004927	0.015540	-0.030042
Long-Stay QM Rating_1.0	-0.060794	-0.098137	0.141423	0.093750	0.010851	0.035162	-0.061587	-0.034526	0.003717	0.022968	...	0.011282	0.329353	-0.008338	0.009275	-0.002965	1.000000	-0.133043	-0.146283	-0.169960	-0.234865
Long-Stay QM Rating_2.0	-0.052735	-0.075848	0.083499	0.046667	-0.004440	-0.000327	-0.033653	-0.006399	-0.006608	0.010546	...	0.022185	0.178982	-0.002927	-0.008193	0.019929	-0.133043	1.000000	-0.192565	-0.223732	-0.309172
Long-Stay QM Rating_3.0	-0.014243	-0.033587	0.064047	0.027324	-0.014332	-0.014127	0.016984	-0.006873	0.002133	0.003653	...	0.009740	0.036916	0.030491	-0.030686	0.004927	-0.146283	-0.192565	1.000000	-0.245998	-0.339940
Long-Stay QM Rating_4.0	-0.000956	0.003190	-0.013288	-0.020436	-0.008354	-0.019080	0.038566	0.007252	-0.028402	-0.009102	...	-0.011606	-0.070261	0.004332	-0.012461	0.015540	-0.169960	-0.223732	-0.245998	1.000000	-0.394961
Long-Stay QM Rating_5.0	0.084292	0.140999	-0.191644	-0.101795	0.015866	0.004862	0.017473	0.014969	0.009778	-0.028530	...	-0.024869	-0.306295	-0.014529	0.029741	-0.030042	-0.234865	-0.309172	-0.339940	-0.394961	1.000000

37 rows × 37 columns

corr2 = sns.heatmap(corr).set_title('Correlation Heatmap')
figure = corr2.get_figure()

Most attributes are not correlated or weakly correlated.
Number of Certified Beds and Average Number of Residents per Day are the only attributes that were strongly correlated > 0.9.
Additionally, it is suspected that the dummy variables of Ownership Type and Long-Stay QM are highly correlated within themselves.
Registered Nurse turnover and Total nursing staff turnover, COVID-19 deaths per occupied beds and confirmed COVID-19 cases per occupied beds, and Percentage of long-stay residents whose need for help with daily activities has increased and Percentage of long-stay residents whose ability to move independently worsened were moderately correlated at 0.67, 0.64 and 0.57 respectively. This will be checked through VIF.

#VIF testing
# temp_df = normalized_df.drop(['Federal Provider Number', 'Provider Name'], axis=1)
temp_df = normalized_df.copy()
temp_df = temp_df.dropna() #Removing NaNs for regression
x = temp_df.drop(['Number of outpatient emergency department visits per 1000 long-stay resident days'], axis=1)
y = temp_df['Number of outpatient emergency department visits per 1000 long-stay resident days']
X = sm.add_constant(x)

from statsmodels.stats.outliers_influence import variance_inflation_factor 
vif = pd.DataFrame()
vif["VIF Factor"] = pd.Series([variance_inflation_factor(X.values, i) for i in range(X.shape[1])], index=X.columns)
vif

C:\Users\erpin\anaconda3\lib\site-packages\statsmodels\regression\linear_model.py:1715: RuntimeWarning: divide by zero encountered in double_scalars
  return 1 - self.ssr/self.centered_tss
C:\Users\erpin\anaconda3\lib\site-packages\statsmodels\stats\outliers_influence.py:193: RuntimeWarning: divide by zero encountered in double_scalars
  vif = 1. / (1. - r_squared_i)

	VIF Factor
const	0.000000
Number of Certified Beds	5.856308
Average Number of Residents per Day	6.119702
Total nursing staff turnover	2.117865
Registered Nurse turnover	2.020368
Adjusted Nurse Aide Staffing Hours per Resident per Day	1.405967
Adjusted LPN Staffing Hours per Resident per Day	1.277591
Adjusted RN Staffing Hours per Resident per Day	1.798623
Number of Facility Reported Incidents	1.245592
Number of Substantiated Complaints	1.725617
Number of Citations from Infection Control Inspections	1.245272
Percentage of high risk long-stay residents with pressure ulcers	1.221291
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	1.232327
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	1.240811
Percentage of long-stay residents experiencing one or more falls with major injury	1.239776
Percentage of long-stay residents who have depressive symptoms	1.099738
Percentage of long-stay residents who lose too much weight	1.100462
Percentage of long-stay residents who received an antianxiety or hypnotic medication	1.206740
Percentage of long-stay residents who received an antipsychotic medication	1.279946
Percentage of long-stay residents who were physically restrained	1.024739
Percentage of long-stay residents whose ability to move independently worsened	1.737529
Percentage of long-stay residents whose need for help with daily activities has increased	1.841184
Percentage of long-stay residents with a catheter inserted and left in their bladder	1.195252
Percentage of long-stay residents with a urinary tract infection	1.330709
Percentage of low risk long-stay residents who lose control of their bowels or bladder	1.139309
Total Number of Health Deficiencies	1.213540
Total Number of Fire Safety Deficiencies	1.105236
Confirmed COVID-19 Cases Per Occupied Beds	1.918721
COVID-19 Deaths Per Occupied Beds	1.845137
Ownership Type_0	inf
Ownership Type_1	inf
Ownership Type_2	inf
Long-Stay QM Rating_1.0	14.241123
Long-Stay QM Rating_2.0	22.790562
Long-Stay QM Rating_3.0	26.710613
Long-Stay QM Rating_4.0	32.394937
Long-Stay QM Rating_5.0	43.611444

Based on the VIF estimation of multicollinearity < 5, most variables are not correlated or mildly correlated. As previously established, Number of Certified Beds and Average Number of Residents per Stay are highly correlated. Therefore, Number of Certified Beds will be dropped from the dataset. Additionally, one of the dummy variable attributes will be dropped for Ownership Type and Long-Stay QM Rating.

#Drop Number of Certified Beds and Ownership Type 2 and Long-Stay QM Rating 5.0 then rerun VIF to validate
X.drop(['Number of Certified Beds', 'Ownership Type_2', 'Long-Stay QM Rating_5.0'], axis=1, inplace=True)
X.head()

	const	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	Number of Substantiated Complaints	Number of Citations from Infection Control Inspections	...	Total Number of Health Deficiencies	Total Number of Fire Safety Deficiencies	Confirmed COVID-19 Cases Per Occupied Beds	COVID-19 Deaths Per Occupied Beds	Ownership Type_0	Ownership Type_1	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0
1	1.0	0.112203	0.493078	0.214	0.361495	0.228712	0.211119	0.000000	0.000000	0.0	...	2.079442	1.386294	0.008457	0.000962	0.0	1.0	0.0	1.0	0.0	0.0
4	1.0	0.101666	0.481363	0.600	0.342242	0.352037	0.090386	0.000000	0.693147	0.0	...	2.079442	1.609438	0.004351	0.000000	0.0	1.0	0.0	0.0	1.0	0.0
5	1.0	0.168162	0.542066	0.526	0.282569	0.172974	0.141020	1.386294	1.386294	0.0	...	1.098612	2.079442	0.017496	0.000000	0.0	1.0	0.0	0.0	0.0	0.0
6	1.0	0.125160	0.603834	0.455	0.312340	0.287205	0.099010	0.000000	1.609438	0.0	...	1.386294	1.609438	0.026687	0.002110	0.0	1.0	0.0	0.0	0.0	0.0
7	1.0	0.144240	0.467519	0.304	0.255430	0.252033	0.202897	1.098612	0.000000	0.0	...	1.609438	1.791759	0.028821	0.007206	0.0	1.0	0.0	0.0	0.0	0.0

5 rows × 34 columns

#Rerunning VIF
vif = pd.DataFrame()
vif["VIF Factor"] = pd.Series([variance_inflation_factor(X.values, i) for i in range(X.shape[1])], index=X.columns)
vif

	VIF Factor
const	5019.422308
Average Number of Residents per Day	1.247418
Total nursing staff turnover	2.115676
Registered Nurse turnover	2.018852
Adjusted Nurse Aide Staffing Hours per Resident per Day	1.400186
Adjusted LPN Staffing Hours per Resident per Day	1.260825
Adjusted RN Staffing Hours per Resident per Day	1.782476
Number of Facility Reported Incidents	1.244090
Number of Substantiated Complaints	1.711102
Number of Citations from Infection Control Inspections	1.242658
Percentage of high risk long-stay residents with pressure ulcers	1.215743
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	1.228979
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	1.240304
Percentage of long-stay residents experiencing one or more falls with major injury	1.232191
Percentage of long-stay residents who have depressive symptoms	1.099570
Percentage of long-stay residents who lose too much weight	1.099758
Percentage of long-stay residents who received an antianxiety or hypnotic medication	1.204532
Percentage of long-stay residents who received an antipsychotic medication	1.273162
Percentage of long-stay residents who were physically restrained	1.024569
Percentage of long-stay residents whose ability to move independently worsened	1.731791
Percentage of long-stay residents whose need for help with daily activities has increased	1.823003
Percentage of long-stay residents with a catheter inserted and left in their bladder	1.191644
Percentage of long-stay residents with a urinary tract infection	1.326707
Percentage of low risk long-stay residents who lose control of their bowels or bladder	1.137648
Total Number of Health Deficiencies	1.209849
Total Number of Fire Safety Deficiencies	1.100916
Confirmed COVID-19 Cases Per Occupied Beds	1.918651
COVID-19 Deaths Per Occupied Beds	1.842216
Ownership Type_0	3.778036
Ownership Type_1	4.028055
Long-Stay QM Rating_1.0	2.178835
Long-Stay QM Rating_2.0	2.143336
Long-Stay QM Rating_3.0	1.866149
Long-Stay QM Rating_4.0	1.572948

Utilizing a VIF indicator of multicollinearity <5, it can be stated that the assumption of reducing multicollinearity is satisfied with the following attributes dropped: 'Number of Certified Beds', 'Ownership Type_2', 'Long-Stay QM Rating_5.0'.

new_df = normalized_df.drop(['Number of Certified Beds', 'Ownership Type_2', 'Long-Stay QM Rating_5.0'], axis=1)
new_df

	Average Number of Residents per Day	Total nursing staff turnover	Registered Nurse turnover	Adjusted Nurse Aide Staffing Hours per Resident per Day	Adjusted LPN Staffing Hours per Resident per Day	Adjusted RN Staffing Hours per Resident per Day	Number of Facility Reported Incidents	Number of Substantiated Complaints	Number of Citations from Infection Control Inspections	Percentage of high risk long-stay residents with pressure ulcers	...	Total Number of Fire Safety Deficiencies	Confirmed COVID-19 Cases Per Occupied Beds	COVID-19 Deaths Per Occupied Beds	Number of outpatient emergency department visits per 1000 long-stay resident days	Ownership Type_0	Ownership Type_1	Long-Stay QM Rating_1.0	Long-Stay QM Rating_2.0	Long-Stay QM Rating_3.0	Long-Stay QM Rating_4.0
0	0.074327	NaN	NaN	NaN	NaN	NaN	0.000000	0.000000	0.000000	0.156756	...	1.098612	0.032455	0.003437	0.049841	0.0	1.0	0.0	0.0	0.0	0.0
1	0.112203	0.493078	0.214	0.361495	0.228712	0.211119	0.000000	0.000000	0.000000	0.315860	...	1.386294	0.008457	0.000962	0.087831	0.0	1.0	0.0	1.0	0.0	0.0
2	0.055389	NaN	NaN	NaN	NaN	NaN	0.000000	0.000000	0.000000	0.160227	...	0.000000	0.009559	0.003020	0.180467	0.0	0.0	0.0	0.0	1.0	0.0
3	0.097394	NaN	NaN	0.293437	0.271050	0.096056	0.000000	0.000000	0.000000	0.157549	...	1.791759	0.014571	0.000000	0.158171	0.0	1.0	0.0	1.0	0.0	0.0
4	0.101666	0.481363	0.600	0.342242	0.352037	0.090386	0.000000	0.693147	0.000000	0.202088	...	1.609438	0.004351	0.000000	0.116917	0.0	1.0	0.0	0.0	1.0	0.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
15216	0.154492	NaN	NaN	NaN	NaN	NaN	0.000000	1.098612	0.000000	0.202819	...	NaN	0.022204	0.005571	0.270040	0.0	0.0	1.0	0.0	0.0	0.0
15217	0.126015	0.282215	0.400	0.243657	0.227983	0.030282	1.609438	1.386294	0.000000	0.165183	...	NaN	0.001894	0.000000	0.087880	0.0	1.0	0.0	0.0	0.0	1.0
15225	0.066353	NaN	NaN	NaN	NaN	NaN	0.000000	0.000000	0.000000	0.264640	...	NaN	0.000000	0.000000	0.121500	0.0	1.0	0.0	0.0	0.0	0.0
15234	0.206180	NaN	NaN	0.343166	0.116700	0.243270	0.000000	0.000000	0.000000	0.081749	...	NaN	0.000869	0.000000	0.061953	0.0	1.0	0.0	0.0	0.0	0.0
15235	0.252741	0.322684	0.452	0.368791	0.104998	0.202933	0.000000	1.098612	1.098612	0.139501	...	NaN	0.004305	0.000175	0.023733	0.0	1.0	0.0	0.0	0.0	0.0

12997 rows × 34 columns

Normality of Error terms

# Create model for testing distribution of errors
temp_df = new_df.copy()
temp_df = temp_df.dropna() #Removing NaNs for regression
x = temp_df.drop(['Number of outpatient emergency department visits per 1000 long-stay resident days'], axis=1)
y = temp_df['Number of outpatient emergency department visits per 1000 long-stay resident days']
X = sm.add_constant(x)
model = sm.OLS(y, X, missing='drop').fit()
model.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.284
Model:	OLS	Adj. R-squared:	0.282
Method:	Least Squares	F-statistic:	119.8
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	08:10:42	Log-Likelihood:	12248.
No. Observations:	9977	AIC:	-2.443e+04
Df Residuals:	9943	BIC:	-2.418e+04
Df Model:	33
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.3030	0.050	6.015	0.000	0.204	0.402
Average Number of Residents per Day	-0.1681	0.012	-14.287	0.000	-0.191	-0.145
Total nursing staff turnover	0.0223	0.006	3.434	0.001	0.010	0.035
Registered Nurse turnover	0.0028	0.005	0.588	0.556	-0.007	0.012
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0082	0.011	0.771	0.441	-0.013	0.029
Adjusted LPN Staffing Hours per Resident per Day	-0.0446	0.009	-5.030	0.000	-0.062	-0.027
Adjusted RN Staffing Hours per Resident per Day	-0.1076	0.013	-7.998	0.000	-0.134	-0.081
Number of Facility Reported Incidents	0.0013	0.001	1.285	0.199	-0.001	0.003
Number of Substantiated Complaints	0.0027	0.001	3.074	0.002	0.001	0.004
Number of Citations from Infection Control Inspections	2.588e-05	0.001	0.022	0.983	-0.002	0.002
Percentage of high risk long-stay residents with pressure ulcers	-0.0399	0.010	-4.119	0.000	-0.059	-0.021
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0075	0.004	-1.739	0.082	-0.016	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0138	0.011	-1.210	0.226	-0.036	0.009
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0012	0.007	-0.165	0.869	-0.015	0.013
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	0.974	0.330	-0.001	0.002
Percentage of long-stay residents who lose too much weight	3.387e-05	0.010	0.003	0.997	-0.019	0.019
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0319	0.007	4.433	0.000	0.018	0.046
Percentage of long-stay residents who received an antipsychotic medication	-0.1227	0.009	-13.739	0.000	-0.140	-0.105
Percentage of long-stay residents who were physically restrained	0.0016	0.003	0.580	0.562	-0.004	0.007
Percentage of long-stay residents whose ability to move independently worsened	-0.1329	0.008	-17.314	0.000	-0.148	-0.118
Percentage of long-stay residents whose need for help with daily activities has increased	-0.1027	0.012	-8.893	0.000	-0.125	-0.080
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0106	0.001	-7.631	0.000	-0.013	-0.008
Percentage of long-stay residents with a urinary tract infection	-0.0057	0.001	-4.587	0.000	-0.008	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0323	0.004	-7.368	0.000	-0.041	-0.024
Total Number of Health Deficiencies	0.0001	0.001	0.115	0.909	-0.002	0.002
Total Number of Fire Safety Deficiencies	-0.0016	0.001	-1.726	0.084	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0202	0.076	0.268	0.789	-0.128	0.168
COVID-19 Deaths Per Occupied Beds	0.0603	0.212	0.284	0.776	-0.356	0.476
Ownership Type_0	-0.0120	0.003	-3.636	0.000	-0.018	-0.006
Ownership Type_1	-0.0030	0.003	-0.943	0.346	-0.009	0.003
Long-Stay QM Rating_1.0	0.1660	0.004	42.936	0.000	0.158	0.174
Long-Stay QM Rating_2.0	0.1083	0.003	36.416	0.000	0.103	0.114
Long-Stay QM Rating_3.0	0.0722	0.003	28.287	0.000	0.067	0.077
Long-Stay QM Rating_4.0	0.0440	0.002	20.676	0.000	0.040	0.048

Omnibus:	3118.422	Durbin-Watson:	1.907
Prob(Omnibus):	0.000	Jarque-Bera (JB):	13859.861
Skew:	1.468	Prob(JB):	0.00
Kurtosis:	7.972	Cond. No.	2.27e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.27e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

Based on preliminary analysis of the regression model, some general observations can be made:

• R^2 = 0.284, which is relatively low
• There are multiple measures with a p-value > 0.05
• The statsmodel regression notes state that there is potentially strong multicollinearity in model due to the condition number

#Visual analysis 
#Create histogram of errors/residuals
sns.histplot(model.resid).set_title('Residual Distribution');

On visual analysis, model residuals seem approximately normal in distribution, with some right skew.

#Create qqplot of residuals 
sm.qqplot(model.resid, line='s');

The qq-plot additionally shows the right-skew.

#Using the Jarque-Bera test to confirm lack of normality in residuals 
stats.jarque_bera(model.resid)

Jarque_beraResult(statistic=13859.860932864438, pvalue=0.0)

The Jarque-Bera test is significant for a test statistic of 13859 which confirms that the model residuals have enough skewness and kurtosis to be signficiantly different from a normal distribution. Thus, the model fails this assumption.

Autocorrelation of Error Terms

#Testing for autocorrelation of model residuals using Durbin-Watson test 
from statsmodels.stats.stattools import durbin_watson
durbin_watson(model.resid)

1.906673615916626

Durbin-Watson test to test autocorrelation of error terms/residuals = 1.9, showing little to no autocorrelation in the model. The errors are independent within the model.

Homoscedasticity

#Testing for homoscedasticity using the Het-Breuschpagan Test
import statsmodels.stats.api as sms
test = sms.het_breuschpagan(model.resid, model.model.exog)
test

(403.99785553969406,
 2.114487020436578e-65,
 12.715528135599122,
 6.188956259637698e-67)

Based on the Breusch-Pagan test (where value 1 is the Lagrange multiplier statistic, and value 2 is the p-value), heteroscedasticity is present within the model. Thus, the residuals are not distributed with equal variance, which means that the results of the regression analysis may not be reliable. To attempt to address this, the dependent variable will be log transformed.

# Recreate model with transformed dependent variable 
temp_df = new_df.copy()
temp_df = temp_df.dropna() #Removing NaNs for regression
x_2 = temp_df.drop(['Number of outpatient emergency department visits per 1000 long-stay resident days'], axis=1)
y_2 = temp_df[['Number of outpatient emergency department visits per 1000 long-stay resident days']].applymap(lambda x: np.log(1+x))
Z = sm.add_constant(x_2)
model_2 = sm.OLS(y_2, Z, missing='drop').fit()
model_2.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.291
Method:	Least Squares	F-statistic:	125.2
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	08:22:21	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.783e+04
Df Residuals:	9943	BIC:	-2.758e+04
Df Model:	33
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2685	0.042	6.321	0.000	0.185	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.270	0.000	-0.161	-0.122
Total nursing staff turnover	0.0194	0.005	3.538	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.685	0.493	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0055	0.009	0.611	0.541	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.015	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.262	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0011	0.001	1.308	0.191	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.270	0.001	0.001	0.004
Number of Citations from Infection Control Inspections	1.959e-05	0.001	0.020	0.984	-0.002	0.002
Percentage of high risk long-stay residents with pressure ulcers	-0.0348	0.008	-4.250	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.805	0.071	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.237	0.216	-0.031	0.007
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0007	0.006	-0.126	0.900	-0.012	0.011
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.117	0.264	-0.000	0.002
Percentage of long-stay residents who lose too much weight	0.0004	0.008	0.043	0.966	-0.016	0.016
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.536	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1057	0.008	-14.024	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.565	0.572	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.688	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.204	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0093	0.001	-7.864	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.844	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.587	0.000	-0.035	-0.021
Total Number of Health Deficiencies	6.905e-05	0.001	0.085	0.932	-0.002	0.002
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.660	0.097	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0265	0.064	0.416	0.678	-0.098	0.151
COVID-19 Deaths Per Occupied Beds	0.0165	0.179	0.092	0.926	-0.334	0.367
Ownership Type_0	-0.0106	0.003	-3.800	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.933	0.351	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	43.702	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.003	37.527	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	29.400	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0386	0.002	21.522	0.000	0.035	0.042

Omnibus:	2044.857	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5385.386
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.837	Cond. No.	2.27e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.27e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

test = sms.het_breuschpagan(model_2.resid, model.model.exog)
test

(405.1410499279618,
 1.2470511741708406e-65,
 12.753032266791552,
 3.570151477006638e-67)

Based on the redone Breusch-Pagan test (where value 1 is the Lagrange multiplier statistic, and value 2 is the p-value), heteroscedasticity continues to be present within the model. Thus, the residuals remain not distributed with equal variance, which means that the results of the regression analysis may not be reliable.

Assumption testing summary:

- Normality of predictor distributions: failed after log transformation of predicator variables <br>
- Linearity of independent and dependant variables: failed <br>
- Mullicolinearity: Passed after removing attributes with high correlation using VIF <br>
- Normality of error terms: Failed due to right shew of error terms<br>
- Autocorrelation of error terms: Passed based on the Durbin-Watson test<br>
- Homoscedasticity: Failed based on the Breusch-Pagan test<br>

The results of assumption testing show that linear regression may not be the ideal test to use for this dataset. Regardless, linear regression will be conducted on the data and the effect of the failed assumptions will be considered in context of the performance of the model.

Model Building

model_2.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.291
Method:	Least Squares	F-statistic:	125.2
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:18	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.783e+04
Df Residuals:	9943	BIC:	-2.758e+04
Df Model:	33
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2685	0.042	6.321	0.000	0.185	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.270	0.000	-0.161	-0.122
Total nursing staff turnover	0.0194	0.005	3.538	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.685	0.493	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0055	0.009	0.611	0.541	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.015	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.262	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0011	0.001	1.308	0.191	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.270	0.001	0.001	0.004
Number of Citations from Infection Control Inspections	1.959e-05	0.001	0.020	0.984	-0.002	0.002
Percentage of high risk long-stay residents with pressure ulcers	-0.0348	0.008	-4.250	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.805	0.071	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.237	0.216	-0.031	0.007
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0007	0.006	-0.126	0.900	-0.012	0.011
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.117	0.264	-0.000	0.002
Percentage of long-stay residents who lose too much weight	0.0004	0.008	0.043	0.966	-0.016	0.016
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.536	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1057	0.008	-14.024	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.565	0.572	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.688	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.204	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0093	0.001	-7.864	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.844	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.587	0.000	-0.035	-0.021
Total Number of Health Deficiencies	6.905e-05	0.001	0.085	0.932	-0.002	0.002
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.660	0.097	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0265	0.064	0.416	0.678	-0.098	0.151
COVID-19 Deaths Per Occupied Beds	0.0165	0.179	0.092	0.926	-0.334	0.367
Ownership Type_0	-0.0106	0.003	-3.800	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.933	0.351	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	43.702	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.003	37.527	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	29.400	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0386	0.002	21.522	0.000	0.035	0.042

Omnibus:	2044.857	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5385.386
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.837	Cond. No.	2.27e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.27e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

Note the following general observations:

• R^2 = 0.294, which remains relatively low
• F-value is statistically significant
• There are multiple measures with a p-value > 0.05
• The statsmodel regression notes state that there is potentially strong multicollinearity in model due to the condition number

Stepwise regression will be performed to increase stability of the model. Alpha = 0.05 so coefficients with p-value > 0.05 will be removed.

#Performing stepwise regression on largest p-value attribute
#Removing 'Percentage of long-stay residents who lose too much weight' - p-value of 0.966
Z_drop = Z.drop(['Percentage of long-stay residents who lose too much weight'], axis=1)
model_3 = sm.OLS(y_2, Z_drop, missing='drop').fit()
model_3.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.291
Method:	Least Squares	F-statistic:	129.1
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:21	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.783e+04
Df Residuals:	9944	BIC:	-2.759e+04
Df Model:	32
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2686	0.042	6.324	0.000	0.185	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.273	0.000	-0.161	-0.122
Total nursing staff turnover	0.0194	0.005	3.540	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.685	0.493	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0054	0.009	0.610	0.542	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.015	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.266	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0011	0.001	1.308	0.191	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.273	0.001	0.001	0.004
Number of Citations from Infection Control Inspections	1.915e-05	0.001	0.019	0.985	-0.002	0.002
Percentage of high risk long-stay residents with pressure ulcers	-0.0347	0.008	-4.265	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.805	0.071	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.237	0.216	-0.031	0.007
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0007	0.006	-0.124	0.902	-0.012	0.011
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.118	0.264	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.540	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1057	0.008	-14.030	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.566	0.571	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.715	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.207	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0093	0.001	-7.867	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.846	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.611	0.000	-0.035	-0.021
Total Number of Health Deficiencies	6.945e-05	0.001	0.085	0.932	-0.002	0.002
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.661	0.097	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0267	0.064	0.421	0.674	-0.098	0.151
COVID-19 Deaths Per Occupied Beds	0.0164	0.179	0.092	0.927	-0.334	0.367
Ownership Type_0	-0.0106	0.003	-3.800	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.933	0.351	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	43.767	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.003	37.543	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	29.416	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0386	0.002	21.530	0.000	0.035	0.042

Omnibus:	2044.929	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5385.831
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.837	Cond. No.	2.27e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.27e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

Model 3: Removing 'Percentage of long-stay residents who lose too much weight' attribute results:

• R^2 remains at 0.294
• Condition number remains at 2.27e+03

#Removing 'Number of Citations from Infection Control Inspections' 
Z_drop_1 = Z_drop.drop(['Number of Citations from Infection Control Inspections'], axis=1)
model_4 = sm.OLS(y_2, Z_drop_1, missing='drop').fit()
model_4.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.291
Method:	Least Squares	F-statistic:	133.3
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:23	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.783e+04
Df Residuals:	9945	BIC:	-2.760e+04
Df Model:	31
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2686	0.042	6.326	0.000	0.185	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.285	0.000	-0.161	-0.122
Total nursing staff turnover	0.0194	0.005	3.543	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.687	0.492	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0054	0.009	0.611	0.542	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.015	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.269	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0011	0.001	1.311	0.190	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.420	0.001	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0347	0.008	-4.267	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.806	0.071	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.238	0.216	-0.031	0.007
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0007	0.006	-0.124	0.902	-0.012	0.011
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.118	0.264	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.540	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1057	0.008	-14.033	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.566	0.571	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.728	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.217	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0093	0.001	-7.868	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.849	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.614	0.000	-0.035	-0.021
Total Number of Health Deficiencies	7.047e-05	0.001	0.087	0.931	-0.002	0.002
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.666	0.096	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0268	0.063	0.422	0.673	-0.098	0.151
COVID-19 Deaths Per Occupied Beds	0.0164	0.179	0.092	0.927	-0.334	0.367
Ownership Type_0	-0.0106	0.003	-3.802	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.933	0.351	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	43.774	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.003	37.545	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	29.420	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0386	0.002	21.534	0.000	0.035	0.042

Omnibus:	2044.958	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5386.060
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.837	Cond. No.	2.26e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.26e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

Model 4: Removing 'Number of Citations from Infection Control Inspections' attribute results:

• R^2 remains at 0.294
• Condition number decreased minimally to 2.26e+03

#Removing 'Total Number of Health Deficiencies' 
Z_drop_2 = Z_drop_1.drop(['Total Number of Health Deficiencies'], axis=1)
model_5 = sm.OLS(y_2, Z_drop_2, missing='drop').fit()
model_5.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.291
Method:	Least Squares	F-statistic:	137.8
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:24	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.783e+04
Df Residuals:	9946	BIC:	-2.761e+04
Df Model:	30
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2688	0.042	6.339	0.000	0.186	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.294	0.000	-0.161	-0.122
Total nursing staff turnover	0.0194	0.005	3.543	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.690	0.490	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0054	0.009	0.609	0.542	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.016	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.269	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0012	0.001	1.332	0.183	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.524	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0347	0.008	-4.270	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.811	0.070	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.238	0.216	-0.031	0.007
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0007	0.006	-0.125	0.900	-0.012	0.011
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.116	0.264	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.540	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1057	0.008	-14.034	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.567	0.571	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.732	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.224	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0093	0.001	-7.870	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.850	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.627	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.673	0.094	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0267	0.063	0.421	0.673	-0.098	0.151
COVID-19 Deaths Per Occupied Beds	0.0166	0.179	0.093	0.926	-0.334	0.367
Ownership Type_0	-0.0106	0.003	-3.804	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.932	0.351	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	43.777	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.003	37.549	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	29.424	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0386	0.002	21.536	0.000	0.035	0.042

Omnibus:	2045.136	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5387.152
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.837	Cond. No.	2.20e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.2e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

Model 5: Removing 'Total Number of Health Deficiencies' attribute results:

• R^2 remains at 0.294
• Condition number reduced slightly at 2.2e+03

#Removing 'COVID-19 Deaths Per Occupied Beds' 
Z_drop_3 = Z_drop_2.drop(['COVID-19 Deaths Per Occupied Beds'], axis=1)
model_6 = sm.OLS(y_2, Z_drop_3, missing='drop').fit()
model_6.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	142.5
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:26	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.783e+04
Df Residuals:	9947	BIC:	-2.762e+04
Df Model:	29
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2688	0.042	6.341	0.000	0.186	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.294	0.000	-0.161	-0.122
Total nursing staff turnover	0.0193	0.005	3.542	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.692	0.489	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0054	0.009	0.607	0.544	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.015	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0937	0.011	-8.276	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0012	0.001	1.329	0.184	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.531	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0347	0.008	-4.270	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.812	0.070	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.240	0.215	-0.031	0.007
Percentage of long-stay residents experiencing one or more falls with major injury	-0.0007	0.006	-0.122	0.903	-0.012	0.011
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.116	0.265	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.540	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1056	0.008	-14.037	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.568	0.570	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.738	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.225	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0093	0.001	-7.869	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.849	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.633	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.677	0.094	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0307	0.047	0.652	0.515	-0.062	0.123
Ownership Type_0	-0.0106	0.003	-3.803	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.933	0.351	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	43.794	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.003	37.554	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	29.431	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0386	0.002	21.537	0.000	0.035	0.042

Omnibus:	2045.692	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5390.402
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.839	Cond. No.	564.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 6: Removing 'COVID-19 Deaths Per Occupied Beds' attribute results:

• R^2 remains at 0.294
• Condition number is not notable

#Removing 'Percentage of long-stay residents experiencing one or more falls with major injury' 
Z_drop_4 = Z_drop_3.drop(['Percentage of long-stay residents experiencing one or more falls with major injury'], axis=1)
model_7 = sm.OLS(y_2, Z_drop_4, missing='drop').fit()
model_7.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	147.7
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:28	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9948	BIC:	-2.763e+04
Df Model:	28
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2686	0.042	6.340	0.000	0.186	0.352
Average Number of Residents per Day	-0.1415	0.010	-14.326	0.000	-0.161	-0.122
Total nursing staff turnover	0.0193	0.005	3.542	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.697	0.486	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0054	0.009	0.608	0.544	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0375	0.007	-5.015	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.283	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0012	0.001	1.331	0.183	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.545	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0346	0.008	-4.283	0.000	-0.050	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.813	0.070	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0119	0.010	-1.238	0.216	-0.031	0.007
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.112	0.266	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.543	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1056	0.008	-14.063	0.000	-0.120	-0.091
Percentage of long-stay residents who were physically restrained	0.0013	0.002	0.570	0.568	-0.003	0.006
Percentage of long-stay residents whose ability to move independently worsened	-0.1144	0.006	-17.820	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0896	0.010	-9.225	0.000	-0.109	-0.071
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0092	0.001	-7.889	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.855	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.660	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.675	0.094	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0308	0.047	0.654	0.513	-0.061	0.123
Ownership Type_0	-0.0106	0.003	-3.805	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.928	0.353	-0.008	0.003
Long-Stay QM Rating_1.0	0.1424	0.003	45.188	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.714	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0632	0.002	30.056	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.812	0.000	0.035	0.042

Omnibus:	2045.678	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5390.476
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.839	Cond. No.	563.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 7: Removing 'Percentage of long-stay residents experiencing one or more falls with major injury' attribute results:

• R^2 remains at 0.294

#Removing 'Percentage of long-stay residents who were physically restrained' 
Z_drop_5 = Z_drop_4.drop(['Percentage of long-stay residents who were physically restrained'], axis=1)
model_8 = sm.OLS(y_2, Z_drop_5, missing='drop').fit()
model_8.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	153.1
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:29	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9949	BIC:	-2.764e+04
Df Model:	27
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2685	0.042	6.338	0.000	0.185	0.352
Average Number of Residents per Day	-0.1414	0.010	-14.316	0.000	-0.161	-0.122
Total nursing staff turnover	0.0192	0.005	3.533	0.000	0.009	0.030
Registered Nurse turnover	0.0028	0.004	0.693	0.488	-0.005	0.011
Adjusted Nurse Aide Staffing Hours per Resident per Day	0.0055	0.009	0.617	0.537	-0.012	0.023
Adjusted LPN Staffing Hours per Resident per Day	-0.0374	0.007	-5.002	0.000	-0.052	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0938	0.011	-8.291	0.000	-0.116	-0.072
Number of Facility Reported Incidents	0.0012	0.001	1.351	0.177	-0.001	0.003
Number of Substantiated Complaints	0.0024	0.001	3.526	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0344	0.008	-4.260	0.000	-0.050	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.824	0.068	-0.014	0.000
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0118	0.010	-1.232	0.218	-0.031	0.007
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.107	0.268	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0276	0.006	4.565	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1053	0.007	-14.057	0.000	-0.120	-0.091
Percentage of long-stay residents whose ability to move independently worsened	-0.1145	0.006	-17.837	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0895	0.010	-9.218	0.000	-0.109	-0.070
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0092	0.001	-7.873	0.000	-0.012	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.858	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.665	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0013	0.001	-1.669	0.095	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0301	0.047	0.640	0.522	-0.062	0.122
Ownership Type_0	-0.0106	0.003	-3.825	0.000	-0.016	-0.005
Ownership Type_1	-0.0025	0.003	-0.949	0.343	-0.008	0.003
Long-Stay QM Rating_1.0	0.1424	0.003	45.188	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.713	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0632	0.002	30.059	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.807	0.000	0.035	0.042

Omnibus:	2046.791	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5394.967
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.840	Cond. No.	563.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 8: Removing 'Percentage of long-stay residents who were physically restrained' attribute results:

• R^2 remains at 0.294

#Removing 'Adjusted Nurse Aide Staffing Hours per Resident per Day' 
Z_drop_6 = Z_drop_5.drop(['Adjusted Nurse Aide Staffing Hours per Resident per Day'], axis=1)
model_9 = sm.OLS(y_2, Z_drop_6, missing='drop').fit()
model_9.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	159.0
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:31	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9950	BIC:	-2.765e+04
Df Model:	26
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2690	0.042	6.350	0.000	0.186	0.352
Average Number of Residents per Day	-0.1416	0.010	-14.351	0.000	-0.161	-0.122
Total nursing staff turnover	0.0190	0.005	3.497	0.000	0.008	0.030
Registered Nurse turnover	0.0029	0.004	0.732	0.464	-0.005	0.011
Adjusted LPN Staffing Hours per Resident per Day	-0.0362	0.007	-5.009	0.000	-0.050	-0.022
Adjusted RN Staffing Hours per Resident per Day	-0.0916	0.011	-8.552	0.000	-0.113	-0.071
Number of Facility Reported Incidents	0.0012	0.001	1.400	0.162	-0.000	0.003
Number of Substantiated Complaints	0.0024	0.001	3.489	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0345	0.008	-4.280	0.000	-0.050	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.807	0.071	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0116	0.010	-1.212	0.225	-0.030	0.007
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.063	0.288	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.558	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1053	0.007	-14.063	0.000	-0.120	-0.091
Percentage of long-stay residents whose ability to move independently worsened	-0.1148	0.006	-17.965	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0894	0.010	-9.209	0.000	-0.108	-0.070
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0092	0.001	-7.855	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.840	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0284	0.004	-7.831	0.000	-0.036	-0.021
Total Number of Fire Safety Deficiencies	-0.0012	0.001	-1.640	0.101	-0.003	0.000
Confirmed COVID-19 Cases Per Occupied Beds	0.0289	0.047	0.614	0.539	-0.063	0.121
Ownership Type_0	-0.0107	0.003	-3.856	0.000	-0.016	-0.005
Ownership Type_1	-0.0027	0.003	-1.019	0.308	-0.008	0.002
Long-Stay QM Rating_1.0	0.1425	0.003	45.248	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.738	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0632	0.002	30.063	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.809	0.000	0.035	0.042

Omnibus:	2048.127	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5400.633
Skew:	1.109	Prob(JB):	0.00
Kurtosis:	5.841	Cond. No.	562.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 9: Removing 'Adjusted Nurse Aide Staffing Hours per Resident per Day' attribute results:

• R^2 remains at 0.294

#Removing 'Confirmed COVID-19 Cases Per Occupied Bed' 
Z_drop_7 = Z_drop_6.drop(['Confirmed COVID-19 Cases Per Occupied Beds'], axis=1)
model_10 = sm.OLS(y_2, Z_drop_7, missing='drop').fit()
model_10.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.294
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	165.4
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:32	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9951	BIC:	-2.765e+04
Df Model:	25
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2697	0.042	6.371	0.000	0.187	0.353
Average Number of Residents per Day	-0.1419	0.010	-14.396	0.000	-0.161	-0.123
Total nursing staff turnover	0.0192	0.005	3.532	0.000	0.009	0.030
Registered Nurse turnover	0.0029	0.004	0.714	0.475	-0.005	0.011
Adjusted LPN Staffing Hours per Resident per Day	-0.0362	0.007	-5.008	0.000	-0.050	-0.022
Adjusted RN Staffing Hours per Resident per Day	-0.0920	0.011	-8.602	0.000	-0.113	-0.071
Number of Facility Reported Incidents	0.0012	0.001	1.401	0.161	-0.000	0.003
Number of Substantiated Complaints	0.0024	0.001	3.510	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0344	0.008	-4.268	0.000	-0.050	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0065	0.004	-1.797	0.072	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0117	0.010	-1.225	0.221	-0.031	0.007
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.046	0.296	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0277	0.006	4.586	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1054	0.007	-14.075	0.000	-0.120	-0.091
Percentage of long-stay residents whose ability to move independently worsened	-0.1148	0.006	-17.969	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0892	0.010	-9.193	0.000	-0.108	-0.070
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0092	0.001	-7.854	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.874	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0284	0.004	-7.829	0.000	-0.036	-0.021
Total Number of Fire Safety Deficiencies	-0.0012	0.001	-1.638	0.101	-0.003	0.000
Ownership Type_0	-0.0107	0.003	-3.855	0.000	-0.016	-0.005
Ownership Type_1	-0.0026	0.003	-0.995	0.320	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	45.269	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.761	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	30.075	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.806	0.000	0.035	0.042

Omnibus:	2047.945	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5400.931
Skew:	1.109	Prob(JB):	0.00
Kurtosis:	5.842	Cond. No.	516.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 10: Removing 'Confirmed COVID-19 Cases Per Occupied Bed' attribute results:

• R^2 remains at 0.294

#Removing 'Registered Nurse turnover' 
Z_drop_8 = Z_drop_7.drop(['Registered Nurse turnover'], axis=1)
model_11 = sm.OLS(y_2, Z_drop_8, missing='drop').fit()
model_11.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.293
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	172.2
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:34	Log-Likelihood:	13947.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9952	BIC:	-2.766e+04
Df Model:	24
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2715	0.042	6.423	0.000	0.189	0.354
Average Number of Residents per Day	-0.1418	0.010	-14.389	0.000	-0.161	-0.122
Total nursing staff turnover	0.0215	0.004	5.027	0.000	0.013	0.030
Adjusted LPN Staffing Hours per Resident per Day	-0.0358	0.007	-4.969	0.000	-0.050	-0.022
Adjusted RN Staffing Hours per Resident per Day	-0.0932	0.011	-8.825	0.000	-0.114	-0.072
Number of Facility Reported Incidents	0.0012	0.001	1.443	0.149	-0.000	0.003
Number of Substantiated Complaints	0.0024	0.001	3.556	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0342	0.008	-4.248	0.000	-0.050	-0.018
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0066	0.004	-1.808	0.071	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0120	0.010	-1.256	0.209	-0.031	0.007
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.027	0.305	-0.001	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0274	0.006	4.552	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1053	0.007	-14.065	0.000	-0.120	-0.091
Percentage of long-stay residents whose ability to move independently worsened	-0.1149	0.006	-17.971	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0890	0.010	-9.177	0.000	-0.108	-0.070
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0092	0.001	-7.873	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0052	0.001	-4.907	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0283	0.004	-7.805	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0012	0.001	-1.654	0.098	-0.003	0.000
Ownership Type_0	-0.0107	0.003	-3.846	0.000	-0.016	-0.005
Ownership Type_1	-0.0026	0.003	-0.980	0.327	-0.008	0.003
Long-Stay QM Rating_1.0	0.1425	0.003	45.266	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.755	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0632	0.002	30.068	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0385	0.002	21.796	0.000	0.035	0.042

Omnibus:	2047.127	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5395.732
Skew:	1.109	Prob(JB):	0.00
Kurtosis:	5.840	Cond. No.	514.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 11: Removing 'Registered Nurse turnover' attribute results:

• R^2 reduced to 0.293

#Removing 'Ownership Type_1' 
Z_drop_9 = Z_drop_8.drop(['Ownership Type_1'], axis=1)
model_12 = sm.OLS(y_2, Z_drop_9, missing='drop').fit()
model_12.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.293
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	179.7
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:35	Log-Likelihood:	13946.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9953	BIC:	-2.767e+04
Df Model:	23
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2669	0.042	6.354	0.000	0.185	0.349
Average Number of Residents per Day	-0.1411	0.010	-14.356	0.000	-0.160	-0.122
Total nursing staff turnover	0.0215	0.004	5.013	0.000	0.013	0.030
Adjusted LPN Staffing Hours per Resident per Day	-0.0353	0.007	-4.914	0.000	-0.049	-0.021
Adjusted RN Staffing Hours per Resident per Day	-0.0912	0.010	-8.799	0.000	-0.112	-0.071
Number of Facility Reported Incidents	0.0013	0.001	1.469	0.142	-0.000	0.003
Number of Substantiated Complaints	0.0024	0.001	3.516	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0347	0.008	-4.315	0.000	-0.051	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0065	0.004	-1.780	0.075	-0.014	0.001
Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine	-0.0118	0.010	-1.228	0.219	-0.031	0.007
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.059	0.290	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0275	0.006	4.568	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1052	0.007	-14.059	0.000	-0.120	-0.091
Percentage of long-stay residents whose ability to move independently worsened	-0.1154	0.006	-18.108	0.000	-0.128	-0.103
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0884	0.010	-9.136	0.000	-0.107	-0.069
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0092	0.001	-7.865	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.863	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0283	0.004	-7.799	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0012	0.001	-1.618	0.106	-0.003	0.000
Ownership Type_0	-0.0084	0.002	-5.401	0.000	-0.011	-0.005
Long-Stay QM Rating_1.0	0.1426	0.003	45.295	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.002	38.821	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	30.123	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.846	0.000	0.035	0.042

Omnibus:	2048.283	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5404.577
Skew:	1.109	Prob(JB):	0.00
Kurtosis:	5.843	Cond. No.	509.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 12: Removing 'Ownership Type_1' attribute results:

• R^2 remains at 0.293

#Removing 'Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine' 
Z_drop_10 = Z_drop_9.drop(['Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine'], axis=1)
model_13 = sm.OLS(y_2, Z_drop_10, missing='drop').fit()
model_13.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.293
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	187.8
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:37	Log-Likelihood:	13945.
No. Observations:	9977	AIC:	-2.784e+04
Df Residuals:	9954	BIC:	-2.768e+04
Df Model:	22
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2196	0.017	13.107	0.000	0.187	0.252
Average Number of Residents per Day	-0.1412	0.010	-14.373	0.000	-0.160	-0.122
Total nursing staff turnover	0.0218	0.004	5.094	0.000	0.013	0.030
Adjusted LPN Staffing Hours per Resident per Day	-0.0357	0.007	-4.966	0.000	-0.050	-0.022
Adjusted RN Staffing Hours per Resident per Day	-0.0916	0.010	-8.839	0.000	-0.112	-0.071
Number of Facility Reported Incidents	0.0013	0.001	1.451	0.147	-0.000	0.003
Number of Substantiated Complaints	0.0024	0.001	3.650	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0343	0.008	-4.262	0.000	-0.050	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0080	0.003	-2.337	0.019	-0.015	-0.001
Percentage of long-stay residents who have depressive symptoms	0.0006	0.001	1.092	0.275	-0.000	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0274	0.006	4.546	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1048	0.007	-14.014	0.000	-0.119	-0.090
Percentage of long-stay residents whose ability to move independently worsened	-0.1149	0.006	-18.067	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0883	0.010	-9.121	0.000	-0.107	-0.069
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0091	0.001	-7.820	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.880	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0282	0.004	-7.768	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0012	0.001	-1.607	0.108	-0.003	0.000
Ownership Type_0	-0.0084	0.002	-5.398	0.000	-0.011	-0.005
Long-Stay QM Rating_1.0	0.1425	0.003	45.283	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.002	38.819	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	30.137	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.841	0.000	0.035	0.042

Omnibus:	2049.608	Durbin-Watson:	1.906
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5412.098
Skew:	1.109	Prob(JB):	0.00
Kurtosis:	5.846	Cond. No.	158.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 13: Removing 'Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine' attribute results:

• R^2 remains at 0.293

#Removing 'Percentage of long-stay residents who have depressive symptoms' 
Z_drop_11 = Z_drop_10.drop(['Percentage of long-stay residents who have depressive symptoms'], axis=1)
model_14 = sm.OLS(y_2, Z_drop_11, missing='drop').fit()
model_14.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.293
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	196.7
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:38	Log-Likelihood:	13945.
No. Observations:	9977	AIC:	-2.785e+04
Df Residuals:	9955	BIC:	-2.769e+04
Df Model:	21
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2216	0.017	13.307	0.000	0.189	0.254
Average Number of Residents per Day	-0.1412	0.010	-14.373	0.000	-0.160	-0.122
Total nursing staff turnover	0.0218	0.004	5.093	0.000	0.013	0.030
Adjusted LPN Staffing Hours per Resident per Day	-0.0371	0.007	-5.263	0.000	-0.051	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0926	0.010	-8.979	0.000	-0.113	-0.072
Number of Facility Reported Incidents	0.0012	0.001	1.424	0.155	-0.000	0.003
Number of Substantiated Complaints	0.0025	0.001	3.765	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0343	0.008	-4.261	0.000	-0.050	-0.018
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0082	0.003	-2.401	0.016	-0.015	-0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0276	0.006	4.585	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1044	0.007	-13.977	0.000	-0.119	-0.090
Percentage of long-stay residents whose ability to move independently worsened	-0.1152	0.006	-18.119	0.000	-0.128	-0.103
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0881	0.010	-9.103	0.000	-0.107	-0.069
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0091	0.001	-7.820	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.885	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0280	0.004	-7.730	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0012	0.001	-1.562	0.118	-0.003	0.000
Ownership Type_0	-0.0084	0.002	-5.421	0.000	-0.011	-0.005
Long-Stay QM Rating_1.0	0.1425	0.003	45.271	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.804	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	30.120	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0385	0.002	21.817	0.000	0.035	0.042

Omnibus:	2047.186	Durbin-Watson:	1.906
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5397.878
Skew:	1.108	Prob(JB):	0.00
Kurtosis:	5.841	Cond. No.	152.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 14: Removing 'Percentage of long-stay residents assessed and appropriately given the seasonal influenza vaccine' attribute results:

• R^2 remains at 0.293

#Removing 'Number of Facility Reported Incidents' 
Z_drop_12 = Z_drop_11.drop(['Number of Facility Reported Incidents'], axis=1)
model_15 = sm.OLS(y_2, Z_drop_12, missing='drop').fit()
model_15.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.293
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	206.4
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:40	Log-Likelihood:	13944.
No. Observations:	9977	AIC:	-2.785e+04
Df Residuals:	9956	BIC:	-2.769e+04
Df Model:	20
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2203	0.017	13.246	0.000	0.188	0.253
Average Number of Residents per Day	-0.1403	0.010	-14.310	0.000	-0.160	-0.121
Total nursing staff turnover	0.0220	0.004	5.151	0.000	0.014	0.030
Adjusted LPN Staffing Hours per Resident per Day	-0.0364	0.007	-5.175	0.000	-0.050	-0.023
Adjusted RN Staffing Hours per Resident per Day	-0.0915	0.010	-8.896	0.000	-0.112	-0.071
Number of Substantiated Complaints	0.0028	0.001	4.531	0.000	0.002	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0344	0.008	-4.285	0.000	-0.050	-0.019
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0079	0.003	-2.326	0.020	-0.015	-0.001
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0271	0.006	4.504	0.000	0.015	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1039	0.007	-13.927	0.000	-0.119	-0.089
Percentage of long-stay residents whose ability to move independently worsened	-0.1150	0.006	-18.093	0.000	-0.127	-0.103
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0886	0.010	-9.154	0.000	-0.108	-0.070
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0091	0.001	-7.790	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0052	0.001	-4.920	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0281	0.004	-7.751	0.000	-0.035	-0.021
Total Number of Fire Safety Deficiencies	-0.0011	0.001	-1.493	0.135	-0.003	0.000
Ownership Type_0	-0.0085	0.002	-5.471	0.000	-0.012	-0.005
Long-Stay QM Rating_1.0	0.1424	0.003	45.258	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0942	0.002	38.816	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	30.127	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.851	0.000	0.035	0.042

Omnibus:	2049.733	Durbin-Watson:	1.905
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5404.389
Skew:	1.110	Prob(JB):	0.00
Kurtosis:	5.842	Cond. No.	151.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 15: Removing 'Number of Facility Reported Incidents' attribute results:

• R^2 remains at 0.293

#Removing 'Total Number of Fire Safety Deficiencies' 
Z_drop_13 = Z_drop_12.drop(['Total Number of Fire Safety Deficiencies'], axis=1)
model_16 = sm.OLS(y_2, Z_drop_13, missing='drop').fit()
model_16.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.293
Model:	OLS	Adj. R-squared:	0.292
Method:	Least Squares	F-statistic:	217.1
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:41	Log-Likelihood:	13943.
No. Observations:	9977	AIC:	-2.785e+04
Df Residuals:	9957	BIC:	-2.770e+04
Df Model:	19
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2187	0.017	13.177	0.000	0.186	0.251
Average Number of Residents per Day	-0.1396	0.010	-14.252	0.000	-0.159	-0.120
Total nursing staff turnover	0.0217	0.004	5.092	0.000	0.013	0.030
Adjusted LPN Staffing Hours per Resident per Day	-0.0358	0.007	-5.093	0.000	-0.050	-0.022
Adjusted RN Staffing Hours per Resident per Day	-0.0911	0.010	-8.858	0.000	-0.111	-0.071
Number of Substantiated Complaints	0.0027	0.001	4.342	0.000	0.001	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0339	0.008	-4.219	0.000	-0.050	-0.018
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0080	0.003	-2.341	0.019	-0.015	-0.001
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0274	0.006	4.561	0.000	0.016	0.039
Percentage of long-stay residents who received an antipsychotic medication	-0.1041	0.007	-13.950	0.000	-0.119	-0.089
Percentage of long-stay residents whose ability to move independently worsened	-0.1149	0.006	-18.083	0.000	-0.127	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0885	0.010	-9.144	0.000	-0.107	-0.069
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0091	0.001	-7.809	0.000	-0.011	-0.007
Percentage of long-stay residents with a urinary tract infection	-0.0051	0.001	-4.863	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0279	0.004	-7.705	0.000	-0.035	-0.021
Ownership Type_0	-0.0086	0.002	-5.509	0.000	-0.012	-0.006
Long-Stay QM Rating_1.0	0.1424	0.003	45.241	0.000	0.136	0.149
Long-Stay QM Rating_2.0	0.0941	0.002	38.809	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0633	0.002	30.133	0.000	0.059	0.067
Long-Stay QM Rating_4.0	0.0386	0.002	21.870	0.000	0.035	0.042

Omnibus:	2051.000	Durbin-Watson:	1.904
Prob(Omnibus):	0.000	Jarque-Bera (JB):	5413.322
Skew:	1.110	Prob(JB):	0.00
Kurtosis:	5.845	Cond. No.	145.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Model 16: Removing 'Total Number of Fire Safety Deficiencies' attribute results:

• R^2 remains at 0.293

P-values are now all significant. Model attributes that are important to accuracy of prediction retained.

#80-20 test/train split
from sklearn.model_selection import train_test_split 
X_train, X_test, y_train, y_test = train_test_split(Z_drop_13, y_2, random_state=0, test_size=0.2)

#Fit the resulting model 
final_model = sm.OLS(y_train, X_train).fit()
final_model.summary()

OLS Regression Results

Dep. Variable:	Number of outpatient emergency department visits per 1000 long-stay resident days	R-squared:	0.296
Model:	OLS	Adj. R-squared:	0.295
Method:	Least Squares	F-statistic:	176.4
Date:	Mon, 07 Mar 2022	Prob (F-statistic):	0.00
Time:	09:16:56	Log-Likelihood:	11157.
No. Observations:	7981	AIC:	-2.227e+04
Df Residuals:	7961	BIC:	-2.213e+04
Df Model:	19
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	0.2093	0.019	10.789	0.000	0.171	0.247
Average Number of Residents per Day	-0.1444	0.011	-13.059	0.000	-0.166	-0.123
Total nursing staff turnover	0.0214	0.005	4.528	0.000	0.012	0.031
Adjusted LPN Staffing Hours per Resident per Day	-0.0327	0.008	-4.172	0.000	-0.048	-0.017
Adjusted RN Staffing Hours per Resident per Day	-0.0823	0.011	-7.251	0.000	-0.105	-0.060
Number of Substantiated Complaints	0.0031	0.001	4.448	0.000	0.002	0.004
Percentage of high risk long-stay residents with pressure ulcers	-0.0346	0.009	-3.835	0.000	-0.052	-0.017
Percentage of long-stay residents assessed and appropriately given the pneumococcal vaccine	-0.0063	0.004	-1.579	0.114	-0.014	0.002
Percentage of long-stay residents who received an antianxiety or hypnotic medication	0.0295	0.007	4.394	0.000	0.016	0.043
Percentage of long-stay residents who received an antipsychotic medication	-0.1043	0.008	-12.491	0.000	-0.121	-0.088
Percentage of long-stay residents whose ability to move independently worsened	-0.1155	0.007	-16.297	0.000	-0.129	-0.102
Percentage of long-stay residents whose need for help with daily activities has increased	-0.0838	0.011	-7.800	0.000	-0.105	-0.063
Percentage of long-stay residents with a catheter inserted and left in their bladder	-0.0080	0.001	-6.158	0.000	-0.011	-0.005
Percentage of long-stay residents with a urinary tract infection	-0.0050	0.001	-4.296	0.000	-0.007	-0.003
Percentage of low risk long-stay residents who lose control of their bowels or bladder	-0.0310	0.004	-7.654	0.000	-0.039	-0.023
Ownership Type_0	-0.0081	0.002	-4.630	0.000	-0.011	-0.005
Long-Stay QM Rating_1.0	0.1435	0.004	40.544	0.000	0.137	0.150
Long-Stay QM Rating_2.0	0.0939	0.003	34.616	0.000	0.089	0.099
Long-Stay QM Rating_3.0	0.0634	0.002	26.903	0.000	0.059	0.068
Long-Stay QM Rating_4.0	0.0385	0.002	19.559	0.000	0.035	0.042

Omnibus:	1579.552	Durbin-Watson:	1.991
Prob(Omnibus):	0.000	Jarque-Bera (JB):	3929.082
Skew:	1.091	Prob(JB):	0.00
Kurtosis:	5.656	Cond. No.	151.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Based on the final model, the attributes with the most effect include:
Average Number of Residents per Day: With a unit increase in Average Residents per Day, there is a -0.144 decrease in the Emergency Department Visit Rate.
Long-Stay QM Rating (1.0): With a unit increase in the 1/5 (or lowest) Long-Stay QM Rating, there is an increase in the Emergency Department Visit Rate.
Percentage of long-stay residents whose need for help with daily activities has increase: With a unit increase in the percentage of long-stay residents who need additional help, there is a -0.1155 decrease in Emergency Dpeartment Visit Rate.
Percentage of long-stay resident who received an antipsychotic medication: With a unit increase in the percentage of patients receiving a anti-psychotic medication, there is a -0.1043 decrease in the Emergency Department Visit rate.

Model Testing

y_pred = final_model.predict(X_test)

y_test = y_test.squeeze()

pred_df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})
pred_df

	Actual	Predicted
12645	0.083056	0.110566
14424	0.025257	0.087418
4928	0.104591	0.133685
5458	0.221801	0.129964
8011	0.070050	0.095571
...	...	...
8013	0.054993	0.113514
7346	0.192367	0.218266
3022	0.045119	0.076212
13971	0.090630	0.122906
12516	0.071836	0.084274

1996 rows × 2 columns

#Visualizing the actual versus predicted values
xax = range(len(y_test))
plt.plot(xax, y_test, label='actual')
plt.plot(xax, y_pred, label='predictions')
plt.title("Stepwise Regression Actual vs. Predictions")
plt.legend()
plt.tight_layout()
plt.savefig('srm_pred.png')
plt.show()

Because the dependent variable was a continuous variable, regression metrics will be used to evaluate the model.

Model Evaluation & Validation

#Calculate evaluation metrics 
from sklearn import metrics
print('MAE', metrics.mean_absolute_error(y_test, y_pred))
print('R^2', metrics.r2_score(y_test, y_pred))
print('RMSE', metrics.mean_squared_error(y_test, y_pred))

MAE 0.04526530738707251
R^2 0.27676391504288367
RMSE 0.0036011681359969148

Mean Absolute Error measures the accuracy of the model. A MAE of 0.045 signifies that the model is generally accurate, and closely able to predict the actual values.
R^2 measures the amount of variation that can be explained by the model and currently is at 27%, which means that only 27% of model predictions are correct.
The Root Mean Squared Error shows the spread of the residual errors. A value of 0.003 shows that the model has good performance.

# Plot residuals to determine variance 
sns.residplot(y_test, y_pred)
plt.show()

C:\Users\erpin\anaconda3\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

Variance of the errors was generally centered around 0.